Covers and envelopes over Gorenstein rings

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概要

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• 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 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.

• 筑波大学の論文
• 1997-01-10

著者

• Edgar E.Enochs

  Instite of Mathematics University of Tsukuba

関連論文

• Covers and envelopes over Gorenstein rings

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