Weak dimensions and Gorenstein weak dimensions of group rings

Abstract

Institute of Mathematics of the Czech Academy of Sciences provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use.This document has been digitized, optimized for electronic delivery and stamped with digital signature within the project DML-CZ: The Czech Digital Mathematics Library http://dml.cz

Five theorems on Gorenstein global dimensions

“…We take the opportunity to include a note on how the Gorenstein flat-cotorsion dimension behaves along certain ring homomorphisms. This leads to an answer to a question of Y. Xiang [27] on the Gorenstein weak global dimension of group rings.…”

“…An important ingredient in the proofs of these results are generalizations of two results due to Holm [18]: We prove in [7,Theorem 2.1] that the flat, Gorenstein flat, and Gorenstein flat-cotorsion dimensions agree for modules of finite injective dimension, and in Theorem 1.2 we show that the injective and Gorenstein injective dimensions agree for modules of finite flat dimension. In the final section, Theorem 5.2 provides an answer to a question of Y. Xiang [27] on the Gorenstein global dimension of group rings.…”