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December 1996 Covers and envelopes over Gorenstein rings
Edgar E. Enochs, Overtoun M.G. Jenda, Jinzhong Xu
Tsukuba J. Math. 20(2): 487-503 (December 1996). DOI: 10.21099/tkbjm/1496163097

Abstract

A module over a Gorenstein ring is said to be Gorenstein injective if it splits under all modules of finite projective dimension. We show that over a Gorenstein ring every module has a Gorenstein injective envelope. We apply this result to the group algebra $\hat{Z}_{\rho}G$ (with $G$ a finite group and $\hat{Z}_{p}$ the ring of $p$-adic integers for some prime $p$) and show that ever finitely generated $\hat{Z}_{p}G$-module has a cover by a lattice. This gives a way of lifting finite dimensional representations of $G$ over $Z/(p)$ to modular representations of $G$ over $\hat{Z}_{p}$.

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Edgar E. Enochs. Overtoun M.G. Jenda. Jinzhong Xu. "Covers and envelopes over Gorenstein rings." Tsukuba J. Math. 20 (2) 487 - 503, December 1996. https://doi.org/10.21099/tkbjm/1496163097

Information

Published: December 1996
First available in Project Euclid: 30 May 2017

zbMATH: 0895.16001
MathSciNet: MR1422636
Digital Object Identifier: 10.21099/tkbjm/1496163097

Rights: Copyright © 1996 University of Tsukuba, Institute of Mathematics

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Vol.20 • No. 2 • December 1996
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