On certain homological invariants of groups

JOURNAL OF ALGEBRA

卷:335

Article

Asadollahi, J.^1,2  Bahlekeh, A.^2,3  Hajizamani, A.^2,4  Salarian, Sh^1,2 

[1] Univ Isfahan, Dept Math, Esfahan, Iran

[2] Inst Res Fundamental Sci IPM, Sch Math, Tehran, Iran

[3] Gonbad e Kavous Univ, Dept Math, Gonbad E Kavous, Iran

[4] Hormozgan Univ, Dept Math, Bandarabbas, Iran

关键词: Homological dimension;    Flat module;    Covering class;   

DOI  :  10.1016/j.jalgebra.2011.03.018

来源: Elsevier

【 摘 要 】

Recently the notions of sfli Gamma, the supremum of the flat lengths of injective Gamma-modules, and silf Gamma, the supremum of the injective lengths of flat Gamma-modules have been studied by some authors. These homological invariants are based on spli and slip invariants of Gedrich and Gruenberg and it is shown that they have enough potential to play an important role in studying homological conjectures in cohomology of groups. In this paper we will study these invariants. It turns out that, for any group Gamma, the finiteness of silf Gamma implies the finiteness of Air, but the converse is not known. We investigate the situation in which sfli Gamma < infinity implies silf Gamma < infinity. The statement holds for example, for groups Gamma with the property that flat Gamma-modules have finite projective dimension. Moreover, we show that the Gorenstein flat dimension of the trivial Z Gamma-module Z, that will be called Gorenstein homological dimension of Gamma, denoted Ghd Gamma, is completely related to these invariants. (c) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

Free