In mathematics, a ring is an algebraic structure consisting of a set with two binary operations called addition and multiplication, which obey the same...

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

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

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...

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

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, 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...

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...

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

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

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

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 ring theory, a branch of mathematics, the zero ring or trivial ring is the unique ring (up to isomorphism) consisting of one element. (Less commonly...

In mathematics, a near-ring (also near ring or nearring) is an algebraic structure similar to a ring but satisfying fewer axioms. Near-rings arise naturally...

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 Boolean ring R is a ring for which x2 = x for all x in R, that is, a ring that consists of only idempotent elements. An example is the...

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...

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...

Saturn has the most extensive and complex ring system of any planet in the Solar System. The rings consist of particles in orbit around the planet made...

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, an annulus (pl.: annuli or annuluses) is the region between two concentric circles. Informally, it is shaped like a ring or a hardware...

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...

Elements of Mathematics (First ed.). Addison-Wesley. ISBN 978-020100644-5. Cohn, P. M. (1968), "Bezout rings and their subrings" (PDF), Mathematical Proceedings...

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...

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