Explore: Ring Theory

In algebra, ring theory is the study of rings, algebraic structures in which addition and multiplication are defined and have similar properties to those

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

or invertible element of a ring is an invertible element for the multiplication of the ring. That is, an element u of a ring R is a unit if there exists

is applied in algebraic number theory and modular representation theory. Hurwitz quaternion order – An example of ring order Reiner (2003) p. 108 Reiner

Ring theory is a concept or paradigm in psychology that recommends a strategy for dealing with the stress a person may feel when someone they encounter

elements of the ring or module and is compatible with the ring multiplication. Modules are very closely related to the representation theory of groups. They

identity element 1 {\displaystyle 1} . A ring is commutative if the multiplication is commutative, and such a ring is a field when every 0 ≠ a ∈ R {\displaystyle

first known as ideal theory, is the branch of algebra that studies commutative rings, their ideals, and modules over such rings. Both algebraic geometry

Ring theory is the branch of mathematics in which rings are studied: that is, structures supporting both an addition and a multiplication operation. This

{\displaystyle V} ⁠. For example, the theory of Gröbner bases was introduced by Bruno Buchberger for ideals in a polynomial ring R = K[x1, ..., xn] over a field