integral domain
1Integral 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… …
2integral 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 …
3integral domain — noun Date: 1937 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 < the integers under the operations of addition and… …
4integral 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… …
5integral domain — Math. a commutative ring in which the cancellation law holds true. [1935 40] * * * …
6Domain — 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… …
7Integral (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… …
8Domain (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… …
9domain — 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 …
10Integral — 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… …
