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Ring theory studies the structure of rings; their representations, or, in different language, modules; special classes of rings (group rings, division rings, universal enveloping algebras); related structures like rngs; as well as an array of properties that prove to be of interest both within the theory itself and for its applications, such as ...
The study of rings originated from the theory of polynomial rings and the theory of algebraic integers. [11] In 1871, Richard Dedekind defined the concept of the ring of integers of a number field. [12] In this context, he introduced the terms "ideal" (inspired by Ernst Kummer's notion of ideal number) and "module" and studied their properties ...
In mathematics, ring theory is the study of rings—algebraic structures in which addition and multiplication are defined and have similar properties to those familiar from the integers The main article for this category is Ring theory .
The related, but distinct, concept of an ideal in order theory is derived from the notion of ideal in ring theory. A fractional ideal is a generalization of an ideal, and the usual ideals are sometimes called integral ideals for clarity.
Diagram of ring theory showing circles of acquaintance and direction of travel for comfort and "dumping" 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. [ 1 ]
A ring isomorphism is a ring homomorphism having a 2-sided inverse that is also a ring homomorphism. One can prove that a ring homomorphism is an isomorphism if and only if it is bijective as a function on the underlying sets. If there exists a ring isomorphism between two rings R and S, then R and S are called isomorphic. Isomorphic rings ...
Earth may have had a ring made up of a broken asteroid over 400 million years ago, a study finds. The Saturn-like feature could explain a climate shift at the time.
A 1915 postcard from one of the pioneers of commutative algebra, Emmy Noether, to E. Fischer, discussing her work in commutative algebra Commutative algebra, first known as ideal theory, is the branch of algebra that studies commutative rings, their ideals, and modules over such rings.