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微分模的Gorenstein投射和内射复形
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作者 侯波 杨士林 《北京工业大学学报》 CAS CSCD 北大核心 2014年第1期156-160,共5页
考虑微分模的Gorenstein同调理论,证明了一个微分模复形C:=((Cn,θn),dn)是Gorenstein投射的(或Gorenstein内射的)当且仅当每个层次的微分模(Cn,θn)都是Gorenstein投射的(或Gorenstein内射的),并且给出了微分模复形的Gorenstein投射维... 考虑微分模的Gorenstein同调理论,证明了一个微分模复形C:=((Cn,θn),dn)是Gorenstein投射的(或Gorenstein内射的)当且仅当每个层次的微分模(Cn,θn)都是Gorenstein投射的(或Gorenstein内射的),并且给出了微分模复形的Gorenstein投射维数和Gorenstein内射维数的刻画. 展开更多
关键词 微分模 gorenstein投射 gorenstein内射 复形
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复形的Cartan-Eilenberg Gorenstein投射维数
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作者 张春霞 翟晓蕊 《西北师范大学学报(自然科学版)》 CAS 北大核心 2016年第3期1-5,共5页
定义了Cartan-Eilenberg(CE)Gorenstein合冲复形,证明了对任意正整数n,复形K是CE Gorenstein n-合冲复形当且仅当它是CE n-合冲复形;给出了复形的CE Gorenstein投射维数的等价刻画.作为应用,证明了具有有限CE Gorenstein投射维数的复形... 定义了Cartan-Eilenberg(CE)Gorenstein合冲复形,证明了对任意正整数n,复形K是CE Gorenstein n-合冲复形当且仅当它是CE n-合冲复形;给出了复形的CE Gorenstein投射维数的等价刻画.作为应用,证明了具有有限CE Gorenstein投射维数的复形存在CE Gorenstein投射预覆盖. 展开更多
关键词 ce gorenstein投射复形 ce gorenstein投射维数 ce gorenstein n-合冲复形 ce n-合冲复形
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Some Remarks on Projective Generators and Injective Cogenerators 被引量:12
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作者 Li LIANG Nan Qing DING Gang YANG 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2014年第12期2063-2078,共16页
In this paper,we give a relationship between projective generators(resp.,injective cogenerators) in the category of R-modules and the counterparts in the category of complexes of R-modules.As a consequence,we get th... In this paper,we give a relationship between projective generators(resp.,injective cogenerators) in the category of R-modules and the counterparts in the category of complexes of R-modules.As a consequence,we get that complexes of W^--Gorenstein modules are actually W-Gorenstein complexes whenever W is a subcategory of R-modules satisfying W⊥W,where W^- is the subcategory of exact complexes with all cycles in W.We also study when all cycles of a W-Gorenstein complexes are W^--Gorenstein modules. 展开更多
关键词 W-gorenstein modules gorenstein projective complexes gorenstein injective complexes projective generators injective cogenerators
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强Gorenstein投射和内射复形(英文)
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作者 张东东 欧阳柏玉 《湖南师范大学自然科学学报》 CAS 北大核心 2012年第4期1-5,共5页
分别研究了Gorenstein投射和内射复形的特殊情况:强Gorenstein投射复形和强Gorenstein内射复形.证明了复形C是Gorenstein投射复形当且仅当它是强Gorenstein投射复形的直和项.同时,证明了若R在左Noetheri-an环下,下有界复形C是强Gorenst... 分别研究了Gorenstein投射和内射复形的特殊情况:强Gorenstein投射复形和强Gorenstein内射复形.证明了复形C是Gorenstein投射复形当且仅当它是强Gorenstein投射复形的直和项.同时,证明了若R在左Noetheri-an环下,下有界复形C是强Gorenstein内射复形当且仅当C是正合的且每一项Ci是强Gorenstein内射R-模. 展开更多
关键词 gorenstein投射(内射)复形 gorenstein投射(内射)复形
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On Ding Projective Complexes 被引量:3
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作者 Gang YANG Xuan Shang DA 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2018年第11期1718-1730,共13页
In the paper, Ding projective modules and Ding projective complexes are considered. In particular, it is proven that Ding projective complexes are precisely the complexes X for which each Xm is a Ding projective R-mod... In the paper, Ding projective modules and Ding projective complexes are considered. In particular, it is proven that Ding projective complexes are precisely the complexes X for which each Xm is a Ding projective R-module for all m ∈ Z. 展开更多
关键词 gorenstein projective modules Ding projective and Ding injective modules Ding projec-tive complexes
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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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强Cartan-Eilenberg Gorenstein投射和内射复形
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作者 翟晓蕊 张春霞 《山东大学学报(理学版)》 CAS CSCD 北大核心 2015年第12期65-72,共8页
定义并研究了Cartan-Eilenberg(CE)Gorenstein投射和CE Gorenstein内射复形的子类:强CE Gorenstein投射和强CE Gorenstein内射复形。通过举例说明其与已有CE复形之间的关系。证明了复形G是CE Gorenstein投射复形当且仅当它是强CE Gorens... 定义并研究了Cartan-Eilenberg(CE)Gorenstein投射和CE Gorenstein内射复形的子类:强CE Gorenstein投射和强CE Gorenstein内射复形。通过举例说明其与已有CE复形之间的关系。证明了复形G是CE Gorenstein投射复形当且仅当它是强CE Gorenstein投射复形的直和项。给出了CE Gorenstein投射复形是强CE Gorenstein投射复形的一些等价条件。 展开更多
关键词 ce gorenstein投射(内射)复形 ce gorenstein投射(内射)复形
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复形的Cartan-Eilenberg Gorenstein AC-同调维数
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作者 张丽英 杨刚 《山东大学学报(理学版)》 CAS CSCD 北大核心 2020年第4期77-84,共8页
研究了Cartan-Eilenberg Gorenstein AC-内射(投射)复形的若干等价刻画。证明了复形G是Cartan-Eilenberg Gorenstein AC-内射(投射)复形当且仅当G具有Cartan-Eilenberg强完全内射(L完全投射)分解。并且研究了复形的Cartan-Eilenberg Gor... 研究了Cartan-Eilenberg Gorenstein AC-内射(投射)复形的若干等价刻画。证明了复形G是Cartan-Eilenberg Gorenstein AC-内射(投射)复形当且仅当G具有Cartan-Eilenberg强完全内射(L完全投射)分解。并且研究了复形的Cartan-Eilenberg Gorenstein AC-内射(投射)维数。 展开更多
关键词 绝对clean模(复形) gorenstein AC-内射(投射)模 Cartan-Eilenberg gorenstein AC-内射(投射)复形
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