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

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

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

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

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...

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

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

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, 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...

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

In mathematics, parity is the property of an integer of whether it is even or odd. An integer is even if it is divisible by 2, and odd if it is not. For...

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 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...

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...

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

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...

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...