Gorenstein Injective and Injective Complete Cohomological Dimensions of Groups

• 作者: Abdolnaser Bahlekeh
• 来源期刊: 代数集刊:英文版
• 学科: 数学
• 关键词: 内射维数 同调维数 ICCD GID 不变量 上同调 函子 引理
• 年，卷（期）: 2015,（3）
• 页码范围: 469-478
• 页数: 10页
• 分类号: O153.3
• 语种: 中文

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.