WebDec 4, 2009 · The concept of a canonical module is of fundamental importance in the study of Cohen–Macaulay local rings. The purpose of this chapter is to introduce the canonical module and derive its basic properties. By definition it is a maximal Cohen–Macaulay module of type 1 and of finite injective dimension. In the first two sections we investigate ... WebQuestions tagged [cohen-macaulay] A ring is called Cohen-Macaulay if its depth is equal to its dimension. More generally, a commutative ring is called Cohen-Macaulay if is Noetherian and all of its localizations at prime ideals are Cohen-Macaulay. In geometric terms, a scheme is called Cohen-Macaulay if it is locally Noetherian and its local ...
arXiv:2106.08583v2 [math.AC] 9 Jun 2024
WebBig Cohen-Macaulay module and algebra closures In my thesis, I studied a mechanism for using big Cohen-Macaulay module and algebra closures to study singularities, and gave many of its properties. De nition Let R be a local ring and B a big Cohen-Macaulay module. For any R-modules N M, we say that x 2Ncl B M if for all b 2B, b x 2im(B R N !B R M): WebStack Exchange network consists of 181 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, … sql int cast
Dualizing module - Wikipedia
WebIt is known that R is a Cohen-Macaulay ring. We are interested in maximal Cohen-Macaulay modules over R which are rigid. Definition 1.1 An R-module M is called rigid if Ext1 R (M,M) = 0. By definition, a rigid module has no nontrivial infinitesimal deformations. Our aim is to classify all the rigid Cohen-Macaulay modules over R up to ... WebIn particular any complete local Cohen–Macaulay ring has a dualizing module. For rings without a dualizing module it is sometimes possible to use the dualizing complex as a substitute. Examples [ edit] If R is a Gorenstein ring, then R considered as a module over itself is a dualizing module. WebAug 4, 2014 · generated R-module M is maximal Cohen–Macaulay if and only if depth R M > d. 2.2. It is well-kn own that the dualizing module Ω gives rise to a duality on the category of sql int check