2022-01-18T10:49:47Zhttps://tsukuba.repo.nii.ac.jp/oaioai:tsukuba.repo.nii.ac.jp:000160692021-03-02T00:52:13ZCovers and envelopes over Gorenstein ringsEnochs, Edgar E.Jenda, Overtoun M.G.Xu, JinzhongA 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 ZpG (with G a finite group and Zp the ring of p-adic integers for some prime p) and show that ever finitely genecrated ZpG-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 Zp.departmental bulletin paperInstitute of Mathematics, University of Tsukuba1996-12application/pdfTsukuba journal of mathematics220487503http://hdl.handle.net/2241/697903874982AA00874643https://tsukuba.repo.nii.ac.jp/record/16069/files/18.pdfeng