Addition and multiplication are viewed as general operations, and their precise definitions lead to structures such as groups, rings and fields
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In mathematics, especially functional analysis, a Banach algebra, named after Stefan Banach, is an associative algebra A over the real or complex numbers which at the same time is also a Banach space
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In mathematics, specifically in ring theory, an algebra over a commutative ring is a generalization of the concept of an algebra over a field, where the base field K is replaced by a commutative ring R. Any ring can be thought of as an algebra over t
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C*-algebras (pronounced "C-star") are an important area of research in functional analysis, a branch of mathematics
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4000 Years of Algebra
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In mathematics, a von Neumann algebra or W*-algebra is a *-algebra of bounded operators on a Hilbert space that is closed in the weak operator topology and contains the identity operator
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an offshoot of first-order logic (and of algebra of sets), deals with a set of relations closed under operators
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In mathematics, specifically in category theory, an F-coalgebra for an endofunctor is an object A of \mathbfC together with a \mathbfC-morphism In this sense F-coalgebras are dual to F-algebras
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In mathematics, specifically in category theory, an F-algebra for an endofunctor is an object A of \mathbfC together with a \mathbfC-morphism In this sense F-algebras are dual to F-coalgebras
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In mathematics, an associative algebra is a vector space (or more generally, a module) which also allows the multiplication of vectors in a distributive and associative manner
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In mathematics, a σ-algebra (sigma is a Greek letter, upper case Σ, lower case σ) over a set X is a nonempty collection Σ of subsets of X (including X itself) that is closed under complementation and countable unions of its members
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the branch of mathematics concerned with the study of vectors, vector spaces (also called linear spaces), linear maps (also called linear transformations), and systems of linear equations
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the subject area of mathematics that studies algebraic structures, such as groups, rings, fields, modules, vector spaces, and algebras
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a fundamental and relatively basic form of algebra taught to students who are presumed to have little or no formal knowledge of mathematics beyond arithmetic
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In abstract algebra, a Boolean algebra or Boolean lattice is a complemented distributive lattice
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the field of mathematics that studies algebraic structures themselves, not examples ("models") of algebraic structures
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system (CAS) is a software program that facilitates symbolic mathematics
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In mathematics, a Lie algebra is an algebraic structure whose main use is in studying geometric objects such as Lie groups and differentiable manifolds
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In mathematics a field of sets is a pair \langle X, \mathcalF \rangle where X is a set and \mathcalF is an algebra over X i.e., a non-empty subset of the power set of X closed under the intersection and union of pairs of sets and under complements of
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In mathematics, Heyting algebras are special partially ordered sets that constitute a generalization of Boolean algebras, named after Arend Heyting
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In mathematics, an algebra over a field K, or a K-algebra, is a vector space A over K equipped with a compatible notion of multiplication of elements of A. A straightforward generalisation allows K to be any commutative ring
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