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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Existence of unliftable modules


Author: David A. Jorgensen
Journal: Proc. Amer. Math. Soc. 127 (1999), 1575-1582
MSC (1991): Primary 13D25, 13H99
Published electronically: February 5, 1999
MathSciNet review: 1476141
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Abstract: Let $(Q,\operatorname{\mathfrak{n}})$ be a commutative Noetherian local ring, and let $R=Q/(x)$ where $x$ is a non-zerodivisor of $Q$ contained in $\operatorname{\mathfrak{n}}$. Then a finitely generated $R$-module $M$ is said to lift to $Q$ if there exists a finitely generated $Q$-module $M'$ such that $x$ is $M'$-regular and $M \cong M'/xM'$. In this paper we give a general construction of finitely generated $R$-modules of finite projective dimension over $R$ which fail to lift to $Q$ provided $x \in \operatorname{\mathfrak{n}}^{2}$ and the depth of $R$ is at least 2.


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Additional Information

David A. Jorgensen
Affiliation: Department of Mathematics, University of Texas, Austin, Texas 78712
Address at time of publication: Department of Mathematics, University of Texas at Arlington, Arlington, Texas 76019
Email: djorgens@math.uta.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-99-04679-1
PII: S 0002-9939(99)04679-1
Keywords: Lifting of modules, free resolution, lifting of complexes, dualized complex
Received by editor(s): June 10, 1997
Received by editor(s) in revised form: September 4, 1997
Published electronically: February 5, 1999
Communicated by: Wolmer V. Vasconcelos
Article copyright: © Copyright 1999 American Mathematical Society