ring theory wikipedia - EAS
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See all on Wikipediahttps://en.wikipedia.org/wiki/Ring_theoryIn algebra, ring theory is the study of rings —algebraic structures in which addition and multiplication are defined and have similar properties to those operations defined for the integers. Ring theory studies the structure of rings, their representations, or, in different language, modules, special classes of rings (group … See more
A ring is called commutative if its multiplication is commutative. Commutative rings resemble familiar number systems, and various definitions for commutative rings are designed to formalize properties of the See more
Dimension of a commutative ring
In this section, R denotes a commutative ring. The Krull dimension of R is the supremum of the lengths n of all the chains of prime ideals . … See moreCommutative ring theory originated in algebraic number theory, algebraic geometry, and invariant theory. Central to the development of these subjects were the rings of integers in algebraic number fields and algebraic function fields, and the rings of polynomials … See more
Noncommutative rings resemble rings of matrices in many respects. Following the model of algebraic geometry, attempts have been made recently at defining noncommutative geometry See more
General
• Isomorphism theorems for rings
• Nakayama's lemma
Structure theorems
• The Artin–Wedderburn theorem determines the … See moreThe ring of integers of a number field
The coordinate ring of an algebraic variety
If X is an affine algebraic variety, then the set of all regular functions on X forms a ring called the coordinate ring of X. For a projective variety, there is an analogous ring called the See moreWikipedia text under CC-BY-SA license- https://en.wikipedia.org/wiki/Ideal_(ring_theory)
In ring theory, a branch of abstract algebra, an ideal of a ring is a special subset of its elements. Ideals generalize certain subsets of the integers, such as the even numbers or the multiples of 3. Addition and subtraction of even numbers preserves evenness, and multiplying an even number by any integer (even or odd) results in an even number; these closure and absorption properties are the defining properties of an ideal. An ideal can be used to construct a quotient ring in a way …
Wikipedia · Text under CC-BY-SA license - https://en.wikipedia.org/wiki/Ring_theory_(psychology)
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, know or love is undergoing crisis. …
- https://en.wikipedia.org/wiki/Unit_(ring_theory)
- In algebra, a unit 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 v in R such that v u = u v = 1, {\displaystyle vu=uv=1,} where 1 is the multiplicative identity; the element v is unique for this property and is called the multiplicative inverse of u. The set of uni...
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Ring Theory - Wikiversity
https://en.wikiversity.org/wiki/Ring_TheoryRing Theory is an extension of Group Theory, vibrant, wide areas of current research in mathematics, computer science and mathematical/theoretical physics. They have many …
- https://brilliant.org/wiki/ring-theory
A ring is a set equipped with two operations (usually referred to as addition and multiplication) that satisfy certain properties: there are additive and multiplicative identities and additive …
- https://en.wikipedia.org/wiki/Glossary_of_ring_theory
Ring theory is the branch of mathematics in which rings are studied: that is, structures supporting both an addition and a multiplication operation. This is a glossary of some terms of the subject. …
- https://simple.wikipedia.org/wiki/Ring_theory
Ring theory is a theory from algebra. In algebra a ring is a structure where multiplication and addition are defined. Rings are similar structures to that of integers . This short article about …
- https://en.wikipedia.org/wiki/Domain_(ring_theory)
Domain (ring theory) In algebra, a domain is a nonzero ring in which ab = 0 implies a = 0 or b = 0. [1] ( Sometimes such a ring is said to "have the zero-product property ".) Equivalently, a …
- https://www.wikiwand.com/en/Ring_theory
Ring theory studies the structure of rings, their representations, or, in different language, modules, special classes of rings , as well as an array of properties that proved to be of interest …
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