A mathematical system that has two operations, usually called addition and multiplication. A ring is an abelian group with respect to addition. Multiplication is associative and distributive with respect to addition.

a fundamental concept in Maths and includes integers, polynomials and matrices as some of the basic examples

an abstract structure in which the objects are subject to two operations (such as addition and multiplication) and satisfy a number of axioms (rules)

an additive commutative group in which a second operation (normally considered as multiplication) is also defined

an algebraic system that it is closed under addition, subtraction, and multiplication (but not necessarily division)

an algebraic system with two operations (addition and multiplication) satisfying various axioms, eg

a set A of objects (such as the integers) that can be added, subtracted and multiplied, but not necessarily divided

a set Sets are one of the most important and fundamental concepts in modern mathematics

a set with two operations, almost always denoted as addition and multiplication

a UFD if and only if its class group In mathematics the theory of algebraic number fields gives rise to a finite abelian group constructed from each such field, its ideal class group

a UFD if and only if its class group is zero

Set of objects, where two operations + and * are defined such that one can calculate like with integers. In general, it is not possible to divide in rings.

In mathematics, a ring is an algebraic structure in which addition and multiplication are defined and have properties listed below. A ring is a generalization of the integers. Other examples include the polynomials and the integers modulo n.