Regular ring
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「Regular ring」文章包含有：「Regularlocalring」、「Section10.106(00NN)」、「VonNeumannregularring」、「RegularRing」、「Regularring(incommutativealgebra)」、「10.110Regularringsandglobaldimension」、「regularlocalringinnLab」、「(PDF)Regularringsandtheirproperties」、「commutativealgebra」、「Regularringsandmodules」
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Regular local ring
https://en.wikipedia.org
A regular local ring is a Noetherian local ring having the property that the minimal number of generators of its maximal ideal is equal to its Krull dimension.
Section 10.106 (00NN)
https://stacks.math.columbia.e
Regular local rings are defined in Definition 10.60.10. It is not that easy to show that all prime localizations of a regular local ring are regular. In fact, ...
Von Neumann regular ring
https://en.wikipedia.org
In mathematics, a von Neumann regular ring is a ring R such that for every element a in R there exists an x in R with a = axa. One may think of x as a weak ...
Regular Ring
https://mathworld.wolfram.com
A regular ring in the sense of commutative algebra is a commutative unit ring such that all its localizations at prime ideals are regular local rings.
Regular ring (in commutative algebra)
https://encyclopediaofmath.org
Fields and Dedekind rings are regular rings. If A is regular, then the ring of polynomials A[X1…Xn] and the ring of formal power series A[[X1…Xn] ...
10.110 Regular rings and global dimension
https://stacks.math.columbia.e
10.110 Regular rings and global dimension. We can use the material on rings of finite global dimension to give another characterization of regular local rings.
regular local ring in nLab
https://ncatlab.org
Every regular local ring is a complete intersection ring and a fortiori a Cohen-Macaulay ring. A useful noncommutative analogue of a regular ...
(PDF) Regular rings and their properties
https://www.researchgate.net
A ring R is called a regular ring if each element in R is regular. Wardayani et al. [17] also studied regular rings and their properties.
commutative algebra
https://math.stackexchange.com
On page 10, a regular ring is defined as Noetherian ring whose every localization at a maximal ideal is a regular local ring. Up until now, ...
Regular rings and modules
https://www.cambridge.org
A left y4-module R will be called (von Neumann) regular iff every submodule is pure. This generalizes the idea of regular ring, as the following theorem shows:.