Integral perfectoid big Cohen–Macaulay algebras via André’s theorem
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DOI: 10.1007/s00208-018-1704-x
Abstract: The main result of this article is to prove that any Noetherian local domain of mixed characteristic maps to an integral perfectoid big Cohen–Macaulay algebra. The proof of this result is based on the construction… read more here.
Keywords: perfectoid big; cohen macaulay; macaulay; big cohen ... See more keywords
The Cohen-Macaulay property of affine semigroup rings in dimension 2
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DOI: 10.1080/00927872.2018.1546392
Abstract: Abstract Consider the subring of , where k is a field and x, y indeterminates over k. We calculate the Hilbert polynomial of . The multiplicity of this ideal provides part of a criterion for… read more here.
Keywords: affine semigroup; cohen macaulay; macaulay; property affine ... See more keywords
About the Cohen-Macaulay defect and almost Cohen-Macaulay rings
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DOI: 10.1142/s0219498826500672
Abstract: We notice the connection between almost Cohen-Macaulay rings and the Cohen-Macaulay defect. We introduce a Serre-type condition for modules, that is connected to the Cohen-Macaulay defect in the same way that the condition $(S_n)$ is… read more here.
Keywords: macaulay defect; macaulay; almost cohen; cohen macaulay ... See more keywords
Residually faithful modules and the Cohen–Macaulay type of idealizations
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DOI: 10.2969/jmsj/80398039
Abstract: The Cohen-Macaulay type of idealizations of maximal Cohen-Macaulay modules over Cohen-Macaulay local rings is explored. There are two extremal cases, one of which is closely related to the theory of Ulrich modules \cite{BHU, GOTWY1, GOTWY2,… read more here.
Keywords: modules cohen; cohen macaulay; macaulay type; macaulay ... See more keywords