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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 $(A, \text{\gotic m})$ 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 $R_{\text{\gotic q}}(M)$ is pseudo Buchsbaum for all parameter ideals $\text{\gotic q}$ of $M$. We also show that the associated graded module $G_{\text{\gotic q}}(M)$ 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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