In mathematics, an order in the sense of ring theory is a subring O {\displaystyle {\mathcal {O}}} of a ring A {\displaystyle A} , such that A {\displaystyle...

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...

order theory, an ideal is a special subset of a partially ordered set (poset). Although this term historically was derived from the notion of a ring ideal...

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...

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...

Order theory is a branch of mathematics that investigates the intuitive notion of order using binary relations. It provides a formal framework for describing...

group or period of an element Order of a polynomial (disambiguation) Order of a square matrix, its dimension Order (ring theory), an algebraic structure Ordered...

of finite rings in their own right has a more recent history. Although rings have more structure than groups do, the theory of finite rings is simpler...

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

In ring theory, a branch of mathematics, an idempotent element or simply idempotent of a ring is an element a such that a2 = a. That is, the element is...

on its properties. Commutative algebra, the theory of commutative rings, is a major branch of ring theory. Its development has been greatly influenced...

supplements introducing the notion of an ideal, fundamental to ring theory. (The word "Ring", introduced later by Hilbert, does not appear in Dedekind's...

theory the elements of Z {\displaystyle \mathbb {Z} } are often called the "rational integers" because of this. The next simplest example is the ring...

In first-order logic, a first-order theory is given by a set of axioms in some language. This entry lists some of the more common examples used in model...

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...

Zero-product property Divisor (ring theory) Integral domain Lam (2001), p. 3 Rowen (1994), p. 99. Some authors also consider the zero ring to be a domain: see Polcino...

number theory, commutative algebra, and algebraic geometry. In ring theory, many classes of rings, such as unique factorization domains, regular rings, group...

Artinian ring – Ring in abstract algebra Countryman line Order theory – Branch of mathematics Permutation – Mathematical version of an order change Prefix...

a ring homomorphism. In this case, f is called a ring isomorphism, and the rings R and S are called isomorphic. From the standpoint of ring theory, isomorphic...

The O-ring theory of economic development is a model of economic development put forward by Michael Kremer in 1993, which proposes that tasks of production...

there are two different notions of a ring of sets, both referring to certain families of sets. In order theory, a nonempty family of sets R {\displaystyle...

product. The corresponding idea in module theory is that of a graded module, namely a left module M over a graded ring R such that M = ⨁ i ∈ N M i , {\displaystyle...

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 an infinity)...

model of it is a ring. The standard axiomatization of P A {\displaystyle {\mathsf {PA}}} is more concise and the theory of its order is commonly treated...

(same as the ring product) and use x ∨ y for the join, given in terms of ring notation (given just above) by x + y + xy. In set theory and logic it is...

thus called a group Hopf algebra. The apparatus of group rings is especially useful in the theory of group representations. Let G {\displaystyle G} be a...

Order theory is a branch of mathematics that studies various kinds of objects (often binary relations) that capture the intuitive notion of ordering, providing...

the ring of integers of K {\displaystyle K} . The order of the group, which is finite, is called the class number of K {\displaystyle K} . The theory extends...

assumed (but not excluded, either). Given an integer n, the ring of real square matrices of order n is an example of an associative algebra over the field...