In commutative algebra, a regular local ring is a Noetherian local ring having the property that the minimal number of generators of its maximal ideal...
12 KB (1,881 words) - 18:55, 4 August 2024
Neumann regular rings should not be confused with the unrelated regular rings and regular local rings of commutative algebra. An element a of a ring is called...
10 KB (1,305 words) - 01:22, 25 November 2023
ring over k. Broadly speaking, regular local rings are somewhat similar to polynomial rings. Regular local rings are UFD's. Discrete valuation rings are...
41 KB (5,655 words) - 15:25, 12 December 2023
older terminology, points with regular local rings were called simple points, and points with geometrically regular local rings were called absolutely simple...
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assumptions, a local ring is Cohen–Macaulay exactly when it is a finitely generated free module over a regular local subring. Cohen–Macaulay rings play a central...
23 KB (3,118 words) - 06:30, 6 July 2024
catenary rings ⊃ Cohen–Macaulay rings ⊃ Gorenstein rings ⊃ complete intersection rings ⊃ regular local rings A local complete intersection ring is a Noetherian...
5 KB (847 words) - 20:37, 15 March 2022
intersection rings ⊃ regular local rings A Gorenstein ring is a commutative Noetherian ring such that each localization at a prime ideal is a Gorenstein local ring...
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Integral domain (redirect from Integral ring)
A regular local ring is an integral domain. In fact, a regular local ring is a UFD. The following rings are not integral domains. The zero ring (the...
20 KB (3,124 words) - 14:07, 23 June 2024
In commutative algebra, a regular sequence is a sequence of elements of a commutative ring which are as independent as possible, in a precise sense. This...
9 KB (1,229 words) - 22:02, 26 September 2019
ring Local ring Noetherian and artinian rings Ordered ring Poisson ring Reduced ring Regular ring Ring of periods SBI ring Valuation ring and discrete...
99 KB (13,632 words) - 06:07, 27 August 2024