**Integral domain** — In abstract algebra, an integral domain is a commutative ring that has no zero divisors,[1] and which is not the trivial ring {0}. It is usually assumed that commutative rings and integral domains have a multiplicative identity even though this… … Wikipedia

**integral domain** — noun A commutative ring with identity not equal to zero which has no zero divisors. Ring R is an integral domain if and only if the polynomial ring is an integral domain … Wiktionary

**integral domain** — noun : a mathematical ring in which multiplication is commutative, which has a multiplicative identity element, and which contains no pair of nonzero elements whose product is zero * * * Math. a commutative ring in which the cancellation law… … Useful english dictionary

**integral domain** — Math. a commutative ring in which the cancellation law holds true. [1935 40] * * * … Universalium

**Domain** — may refer to: General Territory (administrative division), a non sovereign geographic area which has come under the authority of another government Public domain, a body of works and knowledge without proprietary interest Eminent domain, the… … Wikipedia

**Integral (disambiguation)** — Integral may refer to: *constituting, belonging to or making up a whole, necessary for completeness;in mathematics * Of or related to an integer * integral (calculus), the generalization of area, mass, etc. * Integral (measure theory), or… … Wikipedia

**Domain (ring theory)** — In mathematics, especially in the area of abstract algebra known as ring theory, a domain is a ring such that ab = 0 implies that either a = 0 or b = 0.[1] That is, it is a ring which has no left or right zero divisors. (Sometimes such a ring is… … Wikipedia

**domain** — noun Etymology: alteration of Middle English demayne, from Anglo French demeine, from Latin dominium, from dominus Date: 15th century 1. a. complete and absolute ownership of land compare eminent domain … New Collegiate Dictionary

**Integral** — This article is about the concept of integrals in calculus. For the set of numbers, see integer. For other uses, see Integral (disambiguation). A definite integral of a function can be represented as the signed area of the region bounded by its… … Wikipedia

**Integral transform** — In mathematics, an integral transform is any transform T of the following form:: (Tf)(u) = int {t 1}^{t 2} K(t, u), f(t), dt.The input of this transform is a function f , and the output is another function Tf . An integral transform is a… … Wikipedia