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finitely defined algebra

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  • Finitely-generated module — In mathematics, a finitely generated module is a module that has a finite generating set. A finitely generated R module also may be called a finite R module or finite over R.[1] Related concepts include finitely cogenerated modules, finitely… …   Wikipedia

  • Finitely-generated abelian group — In abstract algebra, an abelian group (G,+) is called finitely generated if there exist finitely many elements x1,...,xs in G such that every x in G can be written in the form x = n1x1 + n2x2 + ... + nsxs with integers n1,...,ns. In this case, we …   Wikipedia

  • algebra, modern — ▪ mathematics Introduction also called  abstract algebra        branch of mathematics concerned with the general algebraic structure of various sets (such as real numbers (real number), complex numbers (complex number), matrices (matrix), and… …   Universalium

  • Finitely generated abelian group — In abstract algebra, an abelian group ( G ,+) is called finitely generated if there exist finitely many elements x 1,..., x s in G such that every x in G can be written in the form : x = n 1 x 1 + n 2 x 2 + ... + n s x s with integers n 1,..., n… …   Wikipedia

  • Algebra (ring theory) — 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… …   Wikipedia

  • Boolean algebras canonically defined — Boolean algebras have been formally defined variously as a kind of lattice and as a kind of ring. This article presents them more neutrally but equally formally as simply the models of the equational theory of two values, and observes the… …   Wikipedia

  • Boolean algebra — This article discusses the subject referred to as Boolean algebra. For the mathematical objects, see Boolean algebra (structure). Boolean algebra, as developed in 1854 by George Boole in his book An Investigation of the Laws of Thought,[1] is a… …   Wikipedia

  • Boolean algebra (introduction) — Boolean algebra, developed in 1854 by George Boole in his book An Investigation of the Laws of Thought , is a variant of ordinary algebra as taught in high school. Boolean algebra differs from ordinary algebra in three ways: in the values that… …   Wikipedia

  • Categorical algebra — In category theory, a field of mathematics, a categorical algebra is an associative algebra, defined for any locally finite category and commutative ring with unity.It generalizes the notions of group algebra and incidence algebra,just as… …   Wikipedia

  • Exterior algebra — In mathematics, the exterior product or wedge product of vectors is an algebraic construction generalizing certain features of the cross product to higher dimensions. Like the cross product, and the scalar triple product, the exterior product of… …   Wikipedia

  • Interior algebra — In abstract algebra, an interior algebra is a certain type of algebraic structure that encodes the idea of the topological interior of a set. Interior algebras are to topology and the modal logic S4 what Boolean algebras are to set theory and… …   Wikipedia

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