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

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...

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

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

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

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 matrix (pl.: matrices) is a rectangular array of numbers or other mathematical objects with elements or entries arranged in rows and...

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

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...

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 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...

defining mathematical structure. Those in which a Euclidean division (with remainder) is defined are called Euclidean domains and include polynomial rings in...

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...

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

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...

Algebra is a branch of mathematics that deals with abstract systems, known as algebraic structures, and the manipulation of expressions within those systems...

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...

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, a field is a set on which addition, subtraction, multiplication, and division are defined and behave as the corresponding operations on...

In mathematics, and more specifically in ring theory, an ideal of a ring is a special subset of its elements. Ideals generalize certain subsets of the...