different. Equivalently, a noncommutative ring is a ring that is not a commutative ring. Noncommutative algebra is the part of ring theory devoted to study...
20 KB (2,804 words) - 01:41, 1 November 2023
properties and polynomial identities. Commutative rings are much better understood than noncommutative ones. Algebraic geometry and algebraic number theory...
24 KB (3,098 words) - 08:42, 28 May 2024
Noncommutative geometry (NCG) is a branch of mathematics concerned with a geometric approach to noncommutative algebras, and with the construction of spaces...
21 KB (2,384 words) - 15:46, 26 May 2024
algebraic objects such as rings as well as geometric objects derived from them (e.g. by gluing along localizations or taking noncommutative stack quotients)....
13 KB (1,712 words) - 14:17, 24 June 2023
Prime ideal (redirect from M-system (ring theory))
Abhandl.,3-14. Goodearl, An Introduction to Noncommutative Noetherian Rings Lam, First Course in Noncommutative Rings Obviously, multiplicatively closed sets...
19 KB (2,753 words) - 14:26, 17 July 2024
division rings, and every non-field division ring is noncommutative. The best known example is the ring of quaternions. If one allows only rational instead...
11 KB (1,417 words) - 18:10, 18 November 2023
coordinate ring of an affine algebraic variety, and the ring of integers of a number field. Examples of noncommutative rings include the ring of n × n real...
99 KB (13,632 words) - 08:46, 14 August 2024
Integral domain (redirect from Integral ring)
"domain" for the general case including noncommutative rings. Some sources, notably Lang, use the term entire ring for integral domain. Some specific kinds...
20 KB (3,124 words) - 14:07, 23 June 2024
algebra. Complementarily, noncommutative algebra is the study of ring properties that are not specific to commutative rings. This distinction results...
41 KB (5,655 words) - 15:25, 12 December 2023
Free algebra (redirect from Noncommutative polynomial ring)
area of abstract algebra known as ring theory, a free algebra is the noncommutative analogue of a polynomial ring since its elements may be described...
6 KB (915 words) - 09:19, 17 May 2024