Group ring — This page discusses the algebraic group ring of a discrete group; for the case of a topological group see group algebra, and for a general group see Group Hopf algebra. In algebra, a group ring is a free module and at the same time a ring,… … Wikipedia
Ring (mathematics) — This article is about algebraic structures. For geometric rings, see Annulus (mathematics). For the set theory concept, see Ring of sets. Polynomials, represented here by curves, form a ring under addition and multiplication. In mathematics, a… … Wikipedia
Group cohomology — This article is about homology and cohomology of a group. For homology or cohomology groups of a space or other object, see Homology (mathematics). In abstract algebra, homological algebra, algebraic topology and algebraic number theory, as well… … Wikipedia
Unit (ring theory) — In mathematics, a unit in a (unital) ring R is an invertible element of R , i.e. an element u such that there is a v in R with : uv = vu = 1 R , where 1 R is the multiplicative identity element.That is, u is an invertible element of the… … Wikipedia
Ring theory — In abstract algebra, ring theory is the study of rings algebraic structures in which addition and multiplication are defined and have similar properties to those familiar from the integers. Ring theory studies the structure of rings, their… … Wikipedia
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 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
Ring extension — In mathematics, more specifically in ring theory, a ring extension or extension ring is a ring R with a subring S . We write R / S and say R is a ring extension of S Given an extension R / S of commutative rings and a prime ideal P of R , it… … 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
Formal group — In mathematics, a formal group law is (roughly speaking) a formal power series behaving as if it were the product of a Lie group. They were first defined in 1946 by S. Bochner. The term formal group sometimes means the same as formal group law,… … Wikipedia
Order (ring theory) — In mathematics, an order in the sense of ring theory is a subring of a ring R that satisfies the conditions R is a ring which is a finite dimensional algebra over the rational number field spans R over , so that … Wikipedia