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...

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...

ring over k. Broadly speaking, regular local rings are somewhat similar to polynomial rings. Regular local rings are UFD's. Discrete valuation rings are...

older terminology, points with regular local rings were called simple points, and points with geometrically regular local rings were called absolutely simple...

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...

catenary rings ⊃ Cohen–Macaulay rings ⊃ Gorenstein rings ⊃ complete intersection rings ⊃ regular local rings A local complete intersection ring is a Noetherian...

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...

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...

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...

ring Local ring Noetherian and artinian rings Ordered ring Poisson ring Reduced ring Regular ring Ring of periods SBI ring Valuation ring and discrete...