Gorenstein Injective and Injective Complete Cohomological Dimensions of Groups  

作　　者：Abdolnaser Bahlekeh 

机构地区：[1]Department of Mathematics, Gonbade-Kavous University P.O. Box 49717-99151, Gonbade-Kavous, Iran [2]School of Mathematics, Institute for Research in Fundamental Science (IPM) P.O. Box 19395-5746, Tbhran, Iran

出　　处：《Algebra Colloquium》2015年第3期469-478,共10页代数集刊（英文版）

摘　　要：Using Nucinkis＇s injective complete cohomological functors, we assign a numerical invariant to each group P, called the injective complete cohomological dimension of F, denoted by iccd P. We study this dimension and investigate its properties. Also, we define the Gorenstein injective dimension of the group F, which is denoted by Gid F. We show that Gid F is related to iccd F, as well as to spli and silp invariants of Gedrich and Gruenberg. In particular, it is shown that iccd P is a refinement of Gid P. In addition, we show that silp F = spli F 〈 ∞if and only if the Shapiro lemma holds for injective complete cohomology.Using Nucinkis＇s injective complete cohomological functors, we assign a numerical invariant to each group P, called the injective complete cohomological dimension of F, denoted by iccd P. We study this dimension and investigate its properties. Also, we define the Gorenstein injective dimension of the group F, which is denoted by Gid F. We show that Gid F is related to iccd F, as well as to spli and silp invariants of Gedrich and Gruenberg. In particular, it is shown that iccd P is a refinement of Gid P. In addition, we show that silp F = spli F 〈 ∞if and only if the Shapiro lemma holds for injective complete cohomology.

关 键 词：I-complete cohomology complete injective resolution Gorenstein injective modules 

分 类 号：O153.3[理学—数学] O551.2[理学—基础数学]