In mathematics, rings are algebraic structures that generalize fields: multiplication need not be commutative and multiplicative inverses need not exist...

geometric planar ring Ring (mathematics), an algebraic structure Ring of sets, a family of subsets closed under certain operations Protection ring, in computer...

Ring structure may refer to: Chiastic structure, a literary technique Heterocyclic compound, a chemical structure Ring (mathematics), an algebraic structure...

noncommutative rings, especially noncommutative Noetherian rings. For the definitions of a ring and basic concepts and their properties, see Ring (mathematics). The...

Mathematics is a field of study that discovers and organizes methods, theories and theorems that are developed and proved for the needs of empirical sciences...

Pure mathematics is the study of mathematical concepts independently of any application outside mathematics. These concepts may originate in real-world...

In mathematics, a commutative ring is a ring in which the multiplication operation is commutative. The study of commutative rings is called commutative...

In mathematics, and more specifically in abstract algebra, a rng (or non-unital ring or pseudo-ring) is an algebraic structure satisfying the same properties...

In mathematics, especially in the field of algebra, a polynomial ring or polynomial algebra is a ring formed from the set of polynomials in one or more...

In mathematics, a Noetherian ring is a ring that satisfies the ascending chain condition on left and right ideals; if the chain condition is satisfied...

In mathematics, a module is a generalization of the notion of vector space in which the field of scalars is replaced by a (not necessarily commutative)...

In mathematics, a topological ring is a ring R {\displaystyle R} that is also a topological space such that both the addition and the multiplication are...

In mathematics, the Borromean rings are three simple closed curves in three-dimensional space that are topologically linked and cannot be separated from...

the outset. More generally, matrices with entries in a ring R are widely used in mathematics. Rings are a more general notion than fields in that a division...

mathematics, a product of rings or direct product of rings is a ring that is formed by the Cartesian product of the underlying sets of several rings (possibly...

In mathematics, a ringed space is a family of (commutative) rings parametrized by open subsets of a topological space together with ring homomorphisms...

In mathematics, more specifically in ring theory, local rings are certain rings that are comparatively simple, and serve to describe what is called "local...

In mathematics, the characteristic of a ring R, often denoted char(R), is defined to be the smallest positive number of copies of the ring's multiplicative...

Discrete mathematics is the study of mathematical structures that can be considered "discrete" (in a way analogous to discrete variables, having a bijection...

In mathematics, specifically abstract algebra, an Artinian ring (sometimes Artin ring) is a ring that satisfies the descending chain condition on (one-sided)...

In mathematics, a ring homomorphism is a structure-preserving function between two rings. More explicitly, if R and S are rings, then a ring homomorphism...

form a ring which is the most basic one, in the following sense: for any ring, there is a unique ring homomorphism from the integers into this ring. This...

In mathematics, the category of rings, denoted by Ring, is the category whose objects are rings (with identity) and whose morphisms are ring homomorphisms...

a semiring is an algebraic structure. Semirings are a generalization of rings, dropping the requirement that each element must have an additive inverse...

In mathematics, a noncommutative ring is a ring whose multiplication is not commutative; that is, there exist a and b in the ring such that ab and ba are...

In mathematics, a subring of a ring R is a subset of R that is itself a ring when binary operations of addition and multiplication on R are restricted...

Zbl 0020.34003 Matsumura, Hideyuki (1989), Commutative ring theory, Cambridge Studies in Advanced Mathematics, vol. 8, Translated from the Japanese by Miles Reid...

In mathematics, a semi-local ring is a ring for which R/J(R) is a semisimple ring, where J(R) is the Jacobson radical of R. (Lam 2001, p. §20)(Mikhalev...

In mathematics, the endomorphisms of an abelian group X form a ring. This ring is called the endomorphism ring of X, denoted by End(X); the set of all...

In mathematics, in particular abstract algebra, a graded ring is a ring such that the underlying additive group is a direct sum of abelian groups R i {\displaystyle...