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arXiv · 2506.17717

On sequentially Cohen-Macaulay modules and sequentially generalized Cohen-Macaulay modules

Nguyen Xuan Linh·Le Thanh Nhan
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Abstract

We introduce the notions of sequential sequence and sequential f-sequence in order to characterize sequentially Cohen-Macaulay modules and sequentially generalized Cohen-Macaulay modules. Let R be a Noetherian local ring and M a finitely generated R-module. We show that M is sequentially Cohen-Macaulay (resp. sequentially generalized Cohen-Macaulay) if and only if there exists a system of parameters of M that is an M- sequential sequence (resp. each generalized regular sequence s.o.p of M is an M-sequential f-sequence) and R/AnnR(M) is a quotient of a Cohen-Macaulay local ring. As an application, we give new characterizations of Cohen-Macaulay modules and generalized Cohen-Macaulay modules.

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Nguyen Xuan Linh, Le Thanh Nhan. 2025-06-21. On sequentially Cohen-Macaulay modules and sequentially generalized Cohen-Macaulay modules. https://doi.org/10.1016/j.jalgebra.2025.04.024

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