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n-strongly Gorenstein Projective and Injective and Flat Modules 被引量:3
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作者 YANG Xiao-yan 《Chinese Quarterly Journal of Mathematics》 CSCD 2014年第4期553-564,共12页
In this paper, we study some properties of n-strongly Gorenstein projective,injective and flat modules, and discuss some connections between n-strongly Gorenstein injective, projective and flat modules. Some applicati... In this paper, we study some properties of n-strongly Gorenstein projective,injective and flat modules, and discuss some connections between n-strongly Gorenstein injective, projective and flat modules. Some applications are given. 展开更多
关键词 n-strongly gorenstein projective module n-strongly gorenstein injective module n-strongly gorenstein flat module
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Remarks on Gorenstein Weak Injective and Weak Flat Modules 被引量:6
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作者 Tiwei Zhao Yunge Xu 《Algebra Colloquium》 SCIE CSCD 2020年第4期687-702,共16页
In this paper,we introduce Gorenstein weak injective and weak flat modules in terms of,respectively,weak injective and weak flat modules;the classes of Gorenstein weak injective and weak flat modules are larger than t... In this paper,we introduce Gorenstein weak injective and weak flat modules in terms of,respectively,weak injective and weak flat modules;the classes of Gorenstein weak injective and weak flat modules are larger than the classical classes of Gorenstein injective and flat modules.In this new setting,we characterize rings over which all modules are Gorenstein weak injective.Moreover,we discuss the relation between the weak cosyzygy and Gorenstein weak cosyzygy of a module,and also the stability of Gorenstein weak injective modules. 展开更多
关键词 weak injective module weak flat module gorenstein weak injective module gorenstein weak flat module cosyzygy
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A Note on DG-Gorenstein Injective Complexes 被引量:4
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作者 Bo Lu Kaiyang Lan 《Algebra Colloquium》 SCIE CSCD 2020年第4期731-740,共10页
The notion of DG-Gorenstein injective complexes is studied in this article.It is shown that a complex G is DG-Gorenstein injective if and only if G is exact with Z_(n)(G)Gorenstein injective in R-Mod for each n∈Zand ... The notion of DG-Gorenstein injective complexes is studied in this article.It is shown that a complex G is DG-Gorenstein injective if and only if G is exact with Z_(n)(G)Gorenstein injective in R-Mod for each n∈Zand any morphism f:E→G is null homotopic whenever E is a DG-injective complex. 展开更多
关键词 gorenstein injective module DG-injective complex DG-gorenstein injective complex
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Gorenstein Injective and Injective Complete Cohomological Dimensions of Groups
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作者 Abdolnaser Bahlekeh 《Algebra Colloquium》 SCIE CSCD 2015年第3期469-478,共10页
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 ... 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. 展开更多
关键词 I-complete cohomology complete injective resolution gorenstein injective modules
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Acyclic Complexes and Gorenstein Rings
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作者 Sergio Estrada Alina Iacob Holly Zolt 《Algebra Colloquium》 SCIE CSCD 2020年第3期575-586,共12页
For a given class of modules A,let A be the class of exact complexes having all cycles in A,and dw(A)the class of complexes with all components in A.Denote by GL the class of Gorenstein injective modules.We prove that... For a given class of modules A,let A be the class of exact complexes having all cycles in A,and dw(A)the class of complexes with all components in A.Denote by GL the class of Gorenstein injective modules.We prove that the following are equivalent over any ring R:every exact complex of injective modules is totally acyclic;every exact complex of Gorenstein injective modules is in every complex in dw(GL)is dg-Gorenstein injective.The analogous result for complexes of flat and Gorenstein flat modules also holds over arb计rary rings.If the ring is n-perfect for some integer n≥0,the three equivalent statements for flat and Gorenstein flat modules are equivalent with their counterparts for projective and projectively coresolved Gorenstein flat modules.We also prove the following characterization of Gorenstein rings.Let R be a commutative coherent ring;then the following are equivalent:(1)every exact complex of FP-injective modules has all its cycles Ding injective modules;(2)every exact complex of flat modules is F-totally acyclic,and every R-modulc M such that M^(+)is Gorenstein flat is Ding injective;(3)every exact complex of injectives has all its cycles Ding injective modules and every R-module M such that is Gorenstein flat is Ding injective.If R has finite Krull dimension,statements(1)-(3)are equivalent to(4)R is a Gorenstein ring(in the sense of Iwanaga). 展开更多
关键词 totally acyclic complex gorenstein injective module gorenstein projective module gorenstein flat module Ding injective module
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