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Algebra describing information processing
The term "information algebra" refers to mathematical techniques of information processing. Classical information theory goes back to Claude Shannon.
Information_algebra
American mathematician (1916–2001)
information theory", and the man who laid the foundations of the Information Age. Shannon was among the first to describe the use of Boolean algebra—essential
Claude_Shannon
Branch of mathematics
Algebra is a branch of mathematics that deals with abstract systems, known as algebraic structures, and the manipulation of expressions within those systems
Algebra
Algebraic structure of set algebra
a σ-algebra ("sigma algebra") is part of the formalism for defining sets that can be measured. In calculus and analysis, for example, σ-algebras are used
Σ-algebra
Branch of mathematics
In mathematics, more specifically algebra, abstract algebra or modern algebra is the study of algebraic structures, which are sets with specific operations
Abstract_algebra
Algebraic manipulation of "true" and "false"
mathematics and mathematical logic, Boolean algebra is a branch of algebra. It differs from elementary algebra in two ways. First, the values of the variables
Boolean_algebra
Branch of functional analysis
mechanics, quantum information, and quantum field theory. Operator algebras can be used to study arbitrary sets of operators with little algebraic relation simultaneously
Operator_algebra
Scientific study of digital information
Estimation theory Fisher information Information algebra Information asymmetry Information field theory Information geometry Information theory and measure
Information_theory
Method to convey chess moves
Algebraic notation is the standard method of chess notation, used for recording and describing moves. It is based on a system of coordinates to uniquely
Algebraic_notation_(chess)
Use of conceptual models
Methods for Information Systems Engineering: Knowledge Management and E-Business. Spring 2003 Janis A. Bubenko jr (2007) "From Information Algebra to Enterprise
Systems_modeling
Mathematical software
A computer algebra system (CAS) or symbolic algebra system (SAS) is any mathematical software with the ability to manipulate mathematical expressions in
Computer_algebra_system
Algebraic structure in homological algebra
homological algebra, algebraic topology, and algebraic geometry – a differential graded algebra (or DGA, or DG algebra) is an algebraic structure often
Differential_graded_algebra
Algebra based on a vector space with a quadratic form
mathematics, a Clifford algebra is an algebra generated by a vector space with a quadratic form, and is a unital associative algebra with the additional structure
Clifford_algebra
Algebra can essentially be considered as doing computations similar to those of arithmetic but with non-numerical mathematical objects. However, until
History_of_algebra
Abstract model
a specific IS information algebra. In the 1960s data modeling gained more significance with the initiation of the management information system (MIS) concept
Data_model
Branch of mathematics
through their homology and cohomology. Homological algebra affords the means to extract information contained in these complexes and present it in the
Homological_algebra
Algebra for manipulating geographic data
Map algebra is an algebra for manipulating geographic data, primarily fields. Developed by Dr. Dana Tomlin and others in the late 1970s, it is a set of
Map_algebra
Topological complex vector space
mathematics, specifically in functional analysis, a C∗-algebra (pronounced "C-star") is a Banach algebra together with an involution satisfying the properties
C*-algebra
Algebraic structure designed for geometry
geometric algebra (also known as a Clifford algebra) is an algebra that can represent and manipulate geometrical objects such as vectors. Geometric algebra is
Geometric_algebra
Ring that is also a vector space or a module
In mathematics, an associative algebra A over a commutative ring (often a field) K is a ring A together with a ring homomorphism from K into the center
Associative_algebra
Creator of the XML specification
"ISO/IEC 19845:2015 Information technology -- Universal Business Language Version 2.1 (UBL v2.1)". 11 September 2017. An Information Algebra, Communications
Jon_Bosak
Theory of algebraic structures in general
algebra (sometimes called general algebra) is the field of mathematics that studies algebraic structures in general, not specific types of algebraic structures
Universal_algebra
Algebraic theory
The algebraic theory of topological quantum information is a collection of algebraic techniques developed and applied to topological aspects of condensed
Algebraic theory of topological quantum information
Algebraic_theory_of_topological_quantum_information
American academic
Charles Dana Tomlin is an author, professor, and originator of Map Algebra, a vocabulary and conceptual framework for classifying ways to combine map
Dana_Tomlin
Concept in mathematics
enveloping algebra of a Lie algebra is the unital associative algebra whose representations correspond precisely to the representations of that Lie algebra. Universal
Universal_enveloping_algebra
Overview of and topical guide to algebraic structures
types of algebraic structures are studied. Abstract algebra is primarily the study of specific algebraic structures and their properties. Algebraic structures
Outline of algebraic structures
Outline_of_algebraic_structures
Basic concepts of algebra
{b^{2}-4ac}}}{2a}}}}}} Elementary algebra, also known as high school algebra or college algebra, encompasses the basic concepts of algebra. It is often contrasted
Elementary_algebra
of computer algebra systems (CAS). A CAS is a package comprising a set of algorithms for performing symbolic manipulations on algebraic objects, a language
List of computer algebra systems
List_of_computer_algebra_systems
Linear function satisfying a support condition
enveloping algebra of the Lie algebra of G and thus the construction gives no new information. In the positive characteristic case, the algebra can be used
Distribution on a linear algebraic group
Distribution_on_a_linear_algebraic_group
Algebraic structure with addition, multiplication, and division
operations on rational numbers do. Fields are fundamental algebraic structures that are widely used in algebra, number theory, and many other areas of mathematics
Field_(mathematics)
Branch of mathematics
Algebraic topology is a branch of mathematics that uses tools from abstract algebra to study topological spaces. The basic goal is to find algebraic invariants
Algebraic_topology
Concept in Lie algebra mathematics
In algebra, a simple Lie algebra is a Lie algebra that is non-abelian and contains no nonzero proper ideals. The classification of real simple Lie algebras
Simple_Lie_algebra
"compressing" the information in the algebra. The study of A ∞ {\displaystyle A_{\infty }} -algebras is a subset of homotopical algebra, where there is
Homotopy_associative_algebra
Branch of mathematics
Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometrical problems
Algebraic_geometry
computer algebra system (CAS) is a software product designed for manipulation of mathematical formulae. The principal objective of a computer algebra system
List of open-source software for mathematics
List_of_open-source_software_for_mathematics
Nilpotent subalgebra of a Lie algebra
is a nilpotent subalgebra h {\displaystyle {\mathfrak {h}}} of a Lie algebra g {\displaystyle {\mathfrak {g}}} that is self-normalising (if [ X , Y
Cartan_subalgebra
Measure of a mathematical object studied in the field of algebraic geometry
are purely algebraic and rely on commutative algebra. Some are restricted to algebraic varieties while others apply also to any algebraic set. Some are
Dimension of an algebraic variety
Dimension_of_an_algebraic_variety
Mathematical operation
mathematics, a basic algebraic operation is a mathematical operation similar to any one of the common operations of elementary algebra, which include addition
Algebraic_operation
1969 mathematics textbook
to Commutative Algebra (often informally referred to by the authors' names as "Atiyah and Macdonald") is a well-known commutative algebra textbook written
Introduction to Commutative Algebra
Introduction_to_Commutative_Algebra
Unsolved problem in geometry
asserts that the basic topological information like the number of holes in certain geometric spaces, complex algebraic varieties, can be understood by studying
Hodge_conjecture
Idempotent semiring endowed with a closure operator
In mathematics and theoretical computer science, a Kleene algebra (/ˈkleɪni/ KLAY-nee; named after Stephen Cole Kleene) is a semiring that generalizes
Kleene_algebra
Four-dimensional number system
division algebra over the real numbers. The next extension gives the sedenions, which have zero divisors and so cannot be a normed division algebra. The unit
Quaternion
American mathematician (born 1934)
of Technology Mathematics Department, known for his contributions to algebraic geometry. Artin was born in Hamburg, Germany, and brought up in Indiana
Michael_Artin
Abstract representation of an organization
of data processing". This led to the development of a specific IS information algebra. The first methods dealing with enterprise modelling emerged in the
Enterprise_modelling
Process in linear algebra
In linear algebra, the Schmidt decomposition (named after its originator Erhard Schmidt) refers to a particular way of expressing a vector in the tensor
Schmidt_decomposition
C*-algebra. The various properties of the universal representation are used to obtain information about the ideals and quotients of the C*-algebra. The
Universal representation (C*-algebra)
Universal_representation_(C*-algebra)
Numerical algebraic geometry is a field of computational mathematics, particularly computational algebraic geometry, which uses methods from numerical
Numerical_algebraic_geometry
Branch of mathematics
Derived algebraic geometry is a branch of mathematics that generalizes algebraic geometry to a situation where commutative rings, which provide local charts
Derived_algebraic_geometry
248-dimensional exceptional simple Lie group
several closely related exceptional simple Lie groups, linear algebraic groups or Lie algebras of dimension 248; the same notation is used for the corresponding
E8_(mathematics)
Abstract algebra textbook
Algebra: Chapter 0 is a graduate abstract algebra textbook written by Paolo Aluffi. The book was first published in 2009 by the American Mathematical
Algebra:_Chapter_0
Vertex algebra acted on by the monster group
The monster vertex algebra (or moonshine module) is a vertex algebra acted on by the monster group that was constructed by Igor Frenkel, James Lepowsky
Monster_vertex_algebra
notable theorems. Lists of theorems and similar statements include: List of algebras List of algorithms List of axioms List of conjectures List of data structures
List_of_theorems
In mathematics, a Malcev algebra (or Maltsev algebra or Moufang–Lie algebra) over a field is a nonassociative algebra that is antisymmetric, so that x
Malcev_algebra
Mathematical computing environment
capacity for symbolic computing include those of a general-purpose computer algebra system. For instance, it can manipulate mathematical expressions and find
Maple_(software)
Scientific area at the interface between computer science and mathematics
In mathematics and computer science, computer algebra, also called symbolic computation or algebraic computation, is a scientific area that refers to the
Computer_algebra
In algebra, an operad algebra is an "algebra" over an operad. It is a generalization of an associative algebra over a commutative ring R, with an operad
Operad_algebra
Type of algebra
operator-algebraic information about the given C*-algebra. This is sometimes called the universal enveloping von Neumann algebra, since it is given by
Enveloping von Neumann algebra
Enveloping_von_Neumann_algebra
Generalization of mutual information for more than two variables
interpretation in algebraic topology. The conditional mutual information can be used to inductively define the interaction information for any finite number
Interaction_information
Setting of relativistic physics in geometric algebra
spacetime algebra (STA) is the application of Clifford algebra Cl1,3(R), or equivalently the geometric algebra G(M4) of physics. Spacetime algebra provides
Spacetime_algebra
Middle-school math class in the U.S.
for the study of algebra. Usually, Algebra I is taught in the 8th or 9th grade. As an intermediate stage after arithmetic, pre-algebra helps students pass
Pre-algebra
Notion in statistics
traditional optimality criteria are the information matrix's invariants, in the sense of invariant theory; algebraically, the traditional optimality criteria
Fisher_information
System to capture, manage, and present geographic data
through a process known as "local operation on multiple rasters" or "map algebra", through a function that combines the values of each raster's matrix.
Geographic_information_system
Differential algebra
In abstract algebra, the Weyl algebras are abstracted from the ring of differential operators with polynomial coefficients. They are named after Hermann
Weyl_algebra
Reasoning about equations with free variables
and algebraic description of models appropriate for the study of various logics (in the form of classes of algebras that constitute the algebraic semantics
Algebraic_logic
Algebra with a graded anticommutativity property on multiplication
algebra is a Z-graded algebra for which xy = (−1)deg(x)deg(y)yx for all nonzero homogeneous elements x and y (i.e. it is an anticommutative algebra)
Alternating_algebra
Indexed set in mathematics
representing all historical but not future information available about the stochastic process, with the algebraic structure S i {\displaystyle S_{i}} gaining
Filtration_(mathematics)
Boolean algebra with unary operators expressing necessity and possibility modalities
In algebra and logic, a modal algebra is a structure ⟨ A , ∧ , ∨ , − , 0 , 1 , ◻ ⟩ {\displaystyle \langle A,\land ,\lor ,-,0,1,\Box \rangle } such that
Modal_algebra
dimensional algebras over fields. Projective cover Radical of a module Socle (mathematics) David Eisenbud, Commutative algebra with a view toward Algebraic Geometry
Top_(algebra)
Academic journal
Algebra i Logika (English: Algebra and Logic) is a peer-reviewed Russian mathematical journal founded in 1962 by Anatoly Ivanovich Malcev, published by
Algebra_i_Logika
Boolean algebra with a derivative operator capturing change or boundary behavior
abstract algebra, a derivative algebra is an algebraic structure of the signature <A, ·, +, ', 0, 1, D> where <A, ·, +, ', 0, 1> is a Boolean algebra and D
Derivative algebra (abstract algebra)
Derivative_algebra_(abstract_algebra)
Subring consisting of the elements x
In algebra, the center of a ring R is the subring consisting of the elements x such that xy = yx for all elements y in R. It is a commutative ring and
Center_(ring_theory)
Average uncertainty in variable's states
In information theory, the entropy of a random variable quantifies the average level of uncertainty or information associated with the variable's potential
Entropy_(information_theory)
Associative algebra together with a Lie bracket that satisfies Leibniz's law
In mathematics, a Poisson algebra is an associative algebra together with a Lie bracket that also satisfies Leibniz's law; that is, the bracket is also
Poisson_algebra
Infinite dimensional Lie algebra occurring in quantum field theory
kinematical information – the local symmetry – could still be encoded in an algebra of currents. The commutators involved in current algebra amount to an
Current_algebra
Every polynomial has a real or complex root
The fundamental theorem of algebra, also called d'Alembert's theorem or the d'Alembert–Gauss theorem, states that every non-constant single-variable polynomial
Fundamental theorem of algebra
Fundamental_theorem_of_algebra
In algebra, Freudenthal algebras are certain Jordan algebras constructed from composition algebras. Suppose that C is a composition algebra over a field
Freudenthal_algebra
Type of vector space
In mathematics, the Hecke algebra is the algebra generated by Hecke operators, which are named after Erich Hecke. The algebra is a commutative ring. In
Hecke_algebra
Branch of mathematics that studies abstract algebraic structures
Representation theory is a branch of mathematics that studies abstract algebraic structures by representing their elements as linear transformations of
Representation_theory
Course designed to prepare students for calculus
education, precalculus is a course, or a set of courses, that includes algebra and trigonometry at a level that is designed to prepare students for the
Precalculus
Category of mathematics papers in ArXiv
In mathematics, quantum algebra is the study of noncommutative analogues and generalizations of commutative algebras, especially those arising in Lie theory
Quantum_algebra
Subject area in mathematics
called K-groups. These are groups in the sense of abstract algebra. They contain detailed information about the original object but are notoriously difficult
Algebraic_K-theory
Finding information for an information need
Information retrieval (IR) in computing and information science is the task of identifying and retrieving information system resources that are relevant
Information_retrieval
Concept in mathematics
intermediate between Lie groups (or algebraic groups) and Lie algebras. They are used in algebraic number theory and algebraic topology. A one-dimensional formal
Formal_group_law
of algebra Glossary of field theory Glossary of ring theory List of abstract algebra topics List of algebraic structures List of Boolean algebra topics
Lists_of_mathematics_topics
Mathematical model of quantum mechanics
Effect algebras are partial algebras which abstract the (partial) algebraic properties of events that can be observed in quantum mechanics. Structures
Effect_algebra
Algebraic structure with "nice" duality properties
theory, a Frobenius algebra is a finite-dimensional unital associative algebra with a special kind of bilinear form which gives the algebras particularly nice
Frobenius_algebra
Area of mathematics
algorithm design, computational complexity, numerical methods and computer algebra. Computational mathematics refers also to the use of computers for mathematics
Computational_mathematics
Soviet and Russian mathematician
Springer. ISBN 90-277-2776-7. E. N. Gozodnichev; V. D. Goppa (1995). Algebraic Information Theory (Series on Soviet and East European Mathematics, Vol 11)
Valery_Goppa
Algebraic structure in linear algebra
also a direction. The concept of vector spaces is fundamental for linear algebra, together with the concept of matrices, which allows computing in vector
Vector_space
supersymmetry algebra (or SUSY algebra) is a mathematical formalism for describing the relation between bosons and fermions. The supersymmetry algebra contains
Supersymmetry_algebra
Defunct Google database
which allowed users to add content such as text, images, and structured information in formats such as XML, PDF, Excel, RTF, or WordPerfect. Google Base
Google_Base
In algebra, the Nichols algebra of a braided vector space (with the braiding often induced by a finite group) is a braided Hopf algebra which is denoted
Nichols_algebra
Branch of mathematics
operator-algebraic methods based on C*-algebras, von Neumann algebras, and spectral triples; algebraic approaches to noncommutative rings and graded algebras;
Noncommutative_geometry
International Symposium on Symbolic and Algebraic Computation (ISSAC) is an academic conference in the field of computer algebra. ISSAC has been organized annually
International Symposium on Symbolic and Algebraic Computation
International_Symposium_on_Symbolic_and_Algebraic_Computation
Branch of mathematics
Noncommutative algebraic geometry is a branch of mathematics, and more specifically a direction in noncommutative geometry, that studies the geometric
Noncommutative algebraic geometry
Noncommutative_algebraic_geometry
Concept in mathematics
In mathematics, the special linear Lie algebra of order n {\displaystyle n} over a field F {\displaystyle F} , denoted s l n F {\displaystyle {\mathfrak
Special_linear_Lie_algebra
In algebra, an augmentation of an associative algebra A over a commutative ring k is a k-algebra homomorphism A → k {\displaystyle A\to k} , typically
Augmentation_(algebra)
Notation for quantum states
Bra–ket notation or Dirac notation is a mathematical notation for linear algebra and linear operators on complex vector spaces together with their dual
Bra–ket_notation
Computer algebra system
algebra system. It consists of an interpreter environment, a compiler and a library, which defines a strongly typed hierarchy. Two computer algebra systems
Axiom (computer algebra system)
Axiom_(computer_algebra_system)
Criterion for integration in terms of elementary functions
encode enough information to determine if it can be expressed using elementary functions, the major condition of Liouville's theorem. Algebraic function –
Liouville's theorem (differential algebra)
Liouville's_theorem_(differential_algebra)
travel, tourism, insurance
INFORMATION ALGEBRA
INFORMATION ALGEBRA
INFORMATION ALGEBRA
INFORMATION ALGEBRA
INFORMATION ALGEBRA
INFORMATION ALGEBRA
INFORMATION ALGEBRA
INFORMATION ALGEBRA
INFORMATION ALGEBRA
travel, tourism, insurance