Existence of unliftable modules
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- by David A. Jorgensen PDF
- Proc. Amer. Math. Soc. 127 (1999), 1575-1582 Request permission
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.References
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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
- 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
- © Copyright 1999 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 127 (1999), 1575-1582
- MSC (1991): Primary 13D25, 13H99
- DOI: https://doi.org/10.1090/S0002-9939-99-04679-1
- MathSciNet review: 1476141