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Some characterizations of pseudo Cohen–Macaulay modules
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Let (R, ????) be a Noetherian local ring and M a finitely generated R-module with dim M = d. Following Cuong and the first author [N. T. Cuong and L. T. Nhan, J. Algebra267 (2003) 156–177], M is called pseudo Cohen–Macaulay if [Formula: see text] for a system of parameters [Formula: see text] of M, where [Formula: see text]. In this paper, first we improve some known results on pseudo Cohen–Macaulay modules. Then we study the localizations of pseudo Cohen–Macaulay modules in order to introduce the pseudo Cohen–Macaulayness for the non-local case. Finally, we give characterizations for the formal power series ring and the polynomial ring being pseudo Cohen–Macaulay.
World Scientific Pub Co Pte Lt
Title: Some characterizations of pseudo Cohen–Macaulay modules
Description:
Let (R, ????) be a Noetherian local ring and M a finitely generated R-module with dim M = d.
Following Cuong and the first author [N.
T.
Cuong and L.
T.
Nhan, J.
Algebra267 (2003) 156–177], M is called pseudo Cohen–Macaulay if [Formula: see text] for a system of parameters [Formula: see text] of M, where [Formula: see text].
In this paper, first we improve some known results on pseudo Cohen–Macaulay modules.
Then we study the localizations of pseudo Cohen–Macaulay modules in order to introduce the pseudo Cohen–Macaulayness for the non-local case.
Finally, we give characterizations for the formal power series ring and the polynomial ring being pseudo Cohen–Macaulay.
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