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commutative algebra

См. также в других словарях:

  • Commutative algebra — This page deals with the area of study. For algebras which are commutative, see algebra (disambiguation). Commutative algebra is the branch of abstract algebra that studies commutative rings, their ideals, and modules over such rings. Both… …   Wikipedia

  • commutative algebra — noun : algebra in which the rule of multiplication is such that the product of a by b is the same as the product of b by a …   Useful english dictionary

  • List of commutative algebra topics — Commutative algebra is the branch of abstract algebra that studies commutative rings, their ideals, and modules over such rings. Both algebraic geometry and algebraic number theory build on commutative algebra. Prominent examples of commutative… …   Wikipedia

  • Combinatorial commutative algebra — is a relatively new, rapidly developing mathematical discipline. As the name implies, it lies at the intersection of two more established fields, commutative algebra and combinatorics, and frequently uses methods of one to address problems… …   Wikipedia

  • Minimal prime (commutative algebra) — In mathematics, especially in the area of algebra known as commutative algebra, certain prime ideals called minimal prime ideals play an important role in understanding rings and modules. The notion of height and Krull s Hauptidealsatz use… …   Wikipedia

  • Homological conjectures in commutative algebra — In mathematics, the homological conjectures have been a focus of research activity in commutative algebra since the early 1960s. They concern a number of interrelated (sometimes surprisingly so) conjectures relating various homological properties …   Wikipedia

  • Introduction to Commutative Algebra — is a well known commutative algebra textbook written by Michael Atiyah and Ian G. Macdonald. It deals with elementary concepts of commutative algebra including localization, primary decomposition, integral dependence, Noetherian and Artinian… …   Wikipedia

  • Journal of Commutative Algebra — The Journal of Commutative Algebra is an international mathematical journal publishing research papers and expository articles in commutative algebra and closely related fields including algebraic number theory, algebraic geometry, representation …   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

  • Algebra over a field — This article is about a particular kind of vector space. For other uses of the term algebra , see algebra (disambiguation). In mathematics, an algebra over a field is a vector space equipped with a bilinear vector product. That is to say, it is… …   Wikipedia

  • Commutative ring — In ring theory, a branch of abstract algebra, a commutative ring is a ring in which the multiplication operation is commutative. The study of commutative rings is called commutative algebra. Some specific kinds of commutative rings are given with …   Wikipedia

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