commutative ring

(redirected from Noncommutative ring)

commutative ring

[¦käm·yə‚tād·iv ‚riŋ]
(mathematics)
A ring in which the multiplication obeys the commutative law. Also known as Abelian ring.
References in periodicals archive ?
In Section 5, we make a categorical study of a Morita equivalence of noncommutative ring extensions.
Sugano, On semisimple and separable extensions of noncommutative rings, J.
Objective: As noted by T Y Lam in his book, A first course in noncommutative rings, noncommutative ring theory is a fertile meeting ground for group theory (group rings), representation theory (modules), functional analysis (operator algebras), Lie theory (enveloping algebras), algebraic geometry (finitely generated algebras, differential operators), noncommutative algebraic geometry (graded domains), arithmetic (orders, Brauer groups), universal algebra (co-homology of rings, projective modules) and quantum physics (quantum matrices).
The Principal Investigator, along with two PhD students and two post doctorates, propose to: study basic open questions on infinite dimensional associative noncommutative algebras; pool their expertise so as to tackle problems from a number of related areas of mathematics using noncommutative ring theory, and develop new approaches to existing problems that will benefit future researchers.
Dicho trabajo trata sobre el problema de la estructura de modulos primos, que son una generalizacion del mismo concepto para anillos; de el se derivaron articulos sobre la estructura de modulos y anillos semi-primos, como el capitulo del libro Noncommutative ring theory, titulado Semiprimes modules and rings, publicado por Springer en la serie Lecture Notes in Mathematics en 2006, o el articulo Primal modules, publicado en Commun.
Noncommutative Rings and Their Applications; proceedings
International Conference on Noncommutative Rings and Their Applications (2013: Lens, France) Edited by Steven Dougherty, Alberto Facchini, Andre Leroy, Edmund Puczylowski, and Patrick Sole
Chapters address group theory, commutative rings, Galois theory, noncommutative rings, representation theory, advanced linear algebra, and homology.
Noncommutative rings, group rings, diagram algebras and their applications; proceedings.
Int'l Conference on Noncommutative Rings, Group Rings, Diagram Algebras.