integral closure

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• Integral element — In commutative algebra, an element b of a commutative ring B is said to be integral over its subring A if there are such that That is to say, b is a root of a monic polynomial over A.[1] If B consists of elements that are integral over A, then B… …   Wikipedia

• Closure (mathematics) — For other uses, see Closure (disambiguation). In mathematics, a set is said to be closed under some operation if performance of that operation on members of the set always produces a unique member of the same set. For example, the real numbers… …   Wikipedia

• Closure (container) — For other uses, see Closure (disambiguation). An aluminum bottle with a threaded aluminum screw closure Closures are devices and techniques used to close or seal a bottle, jug, jar, tube, can, etc. Closures can be a cap, cover, lid, plug, etc.… …   Wikipedia

• Cauchy's integral formula — In mathematics, Cauchy s integral formula, named after Augustin Louis Cauchy, is a central statement in complex analysis. It expresses the fact that a holomorphic function defined on a disk is completely determined by its values on the boundary… …   Wikipedia

• Regulated integral — In mathematics, the regulated integral is a definition of integration for regulated functions, which are defined to be uniform limits of step functions. The use of the regulated integral instead of the Riemann integral has been advocated by… …   Wikipedia

• Close, Closed, Closure — סגר ﺇﻏﻼﻖ Close, Closed, Closure Najwa Sultan in Close, Closed, Closure. Directed by Ram Loevy …   Wikipedia

• Cauchy's integral theorem — In mathematics, the Cauchy integral theorem in complex analysis, named after Augustin Louis Cauchy, is an important statement about line integrals for holomorphic functions in the complex plane. Essentially, it says that if two different paths… …   Wikipedia

• Skorokhod integral — In mathematics, the Skorokhod integral, often denoted delta; , is an operator of great importance in the theory of stochastic processes. It is named after the Ukrainian mathematician Anatoliy Skorokhod. Part of its importance is that it unifies… …   Wikipedia

• Integrality — In commutative algebra, the notions of an element integral over a ring (also called an algebraic integer over the ring), and of an integral extension of rings, are a generalization of the notions in field theory of an element being algebraic over …   Wikipedia

• Dedekind domain — In abstract algebra, a Dedekind domain or Dedekind ring, named after Richard Dedekind, is an integral domain in which every nonzero proper ideal factors into a product of prime ideals. It can be shown that such a factorization is then necessarily …   Wikipedia

• Integrally closed domain — In commutative algebra, an integrally closed domain A is an integral domain whose integral closure in the field of fractions of A is A itself. Many well studied domains are integrally closed: Fields, the ring of integers Z, unique factorization… …   Wikipedia