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Vietnam Journal of Mathematics 34:4(2006) 449-458

A Blowing-up Characterization of Pseudo Buchsbaum Modules 

Nguyen Tu Cuong and Nguyen Thi Hong Loan

Abstract.  Let (A, gotic m) be a commutative Noetherian local ring and M a finitely generated A-module. The aim of this paper is to give a blow-up characterization of pseudo Buchsbaum modules defined in [2], which says that M is a pseudo Buchsbaum module if and only if the Rees module R_{gotic q}(M) is pseudo Buchsbaum for all parameter ideals gotic q of M. We also show that the associated graded module G_{gotic q}(M) is pseudo Cohen Macaulay (resp. pseudo Buchsbaum) provided M is pseudo Cohen Macaulay (resp. pseudo Buchsbaum).

2000 Mathematics Subject Classification: 13H10, 13A30.

Keywords: Pseudo Cohen-Macaulay module, pseudo Buchsbaum module, Rees module, associate graded module.

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Published by Springer since January 2013