共查询到20条相似文献,搜索用时 93 毫秒
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本文研究了p-可除kG-模,这是一类由群阶的素数因子来控制的模类.利用Heller算子,证明了n次Heller算子置换非投射不可分解p-可除kG-模的同类;利用模的诱导和限制方法,证明了若H是G的强p-嵌入子群,则Green对应建立了不可分解p-可除kG-模的同构类与不可分解p-可除kH-模的同构类之间的一一对应.推广了不可分解相对投射kG-模上的Green对应. 相似文献
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本文研究了对于给定的一个三角范畴的上(下)粘合(C'',C,C"),如何由C的一个t-结构诱导C''和C"的t-结构的问题.利用左(右)t-正合函子的概念,给出了由C的一个t-结构可诱导出C''和C"的t-结构的充分条件.将粘合的一些相关结果推广到了上(下)粘合的情形. 相似文献
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设R是分次环,本文引入并研究Gorenstein FP-gr-内射模.我们讨论Gorenstein FP-gr-内射模和Gorenstein gr-内射模以及Gorenstein gr-平坦模的关系,刻画Gorenstein FP-gr-内射模的诸多性质,并利用Gorenstein FP-gr-内射模刻画几类熟知的分次环.最后还讨论Gorenstein FP-内射模在分次与未分次情形的联系. 相似文献
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讨论了Gorensteincotorsion模与内射模之间的关系,证明了R是GorensteinvonNeumann正则环当且仅当任意R模M的Oorensteincotorsion包络与内射包络是同构的,当且仅当E(M)/M是Gorenstein平坦模,同时,也讨论了Gorensteincotorsion模与cotorsion模之间的联系。 相似文献
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设H是域k上的有限维Hopf代数,A是左H-模代数.本文研究了Gorenstein平坦(余挠)维数在A-模范畴和A#H-模范畴之间的关系.利用可分函子的性质,证明了(1)设A是右凝聚环,若A#H/A可分且φ:A→A#H是可裂的(A,A)-双模同态,则l:Gwd(A)=l:Gwd(A#H);(2)若A#H/A可分且φ:A→A#H是可裂的(A,A)-双模同态,则l:Gcd(A)=l:Gcd(A#H),推广了斜群环上的结果. 相似文献
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研究了$(m,d)$-内射$R$-模作成的类是(预)盖类的条件,证明了$(m,d)$-凝聚环上的每一个左$R$-模都具有$(m,d)$-内射盖.在此基础上,又引入研究了Gorenstein $(m,d)$-平坦模和Gorenstein $(m,d)$-内射模,证明了$(m,d)$-凝聚环上的左$R$-模$M$是Gorenstein$(m,d)$-平坦模的充分必要条件是它的特征模$M^{+}$是Gorenstein $(m,d)$-内射模.推广了Goresntein平坦模和Goresntein $n$-平坦模上的一些结果. 相似文献
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设n 是正整数, 本文引入并研究n- 强Gorenstein FP- 内射模. 对于正整数n > m, 给出例子说明n- 强Gorenstein FP- 内射模未必是m- 强Gorenstein FP- 内射的, 并讨论n- 强Gorenstein FP-内射模的诸多性质. 最后, 利用n- 强Gorenstein FP- 内射模刻画n- 强Gorenstein Von Neumann 正则环. 相似文献
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In this article, we introduce the concept of IFP-flat (resp., IFP-injective) modules as nontrivial generalization of flat (resp., injective) modules. We investigate the properties of these modules in various ways. For example, we show that the class of IFP-flat (resp., IFP-injective) modules is closed under direct products and direct sums. Therefore, the direct product of flat modules is not flat in general; however, the direct product of flat modules is IFP-flat over any ring. We prove that (⊥??, ??) is a complete cotorsion theory and (??, ??⊥) is a perfect cotorsion theory, where ?? stands for the class of all IFP-injective left R-modules, and ?? denotes the class of all IFP-flat right R-modules. 相似文献
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Let R be a commutative (possibly non-Noetherian) ring (in order to make things less technical) and C a semidualizing R-module. In this article, we introduce and investigate the notion of G C -injective (G C -projective) complexes. This extends Enochs and García Rozas's notion of Gorenstein injective (Gorenstein projective) complexes. We then show that a complex X is G C -injective (G C -projective) if and only if X m is a G C -injective (G C -projective) module for each m ∈ ?. 相似文献
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We study the concepts of the 𝒫C-projective and the ?C-injective dimensions of a module in the noncommutative case, weakening the condition of C being semidualizing. We give the relations between these dimensions and the C-relative Gorenstein dimensions (GC-projective and GC-injective dimensions) of the module. Finally, we compare, in some circumstances, the global 𝒫C-projective dimension of a ring and the global dimension of the endomorphisms ring of C. 相似文献
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Driss Bennis J. R. García Rozas Luis Oyonarte 《Mediterranean Journal of Mathematics》2016,13(1):65-91
In the last years (Gorenstein) homological dimensions relative to a semidualizing module C have been subject of several works as interesting extensions of (Gorenstein) homological dimensions. In this paper, we extend to the noncommutative case the concepts of G C -projective module and dimension, weakening the condition of C being semidualizing as well. We prove that indeed they share the principal properties of the classical ones and relate this new dimension with the classical Gorenstein projective dimension of a module. The dual concepts of G C -injective modules and dimension are also treated. Finally, we show some interesting interactions between the class of G C -projective modules and the Bass class associated to C on one side, and the class of G\({_{C^{\vee}}}\) -injective modules (C ∨ = Hom R (C, E) where E is an injective cogenerator in R-Mod) and the Auslander class associated to C in the other. 相似文献
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Guoqiang Zhao 《代数通讯》2013,41(8):3044-3062
In this article, we study the relation between m-strongly Gorenstein projective (resp., injective) modules and n-strongly Gorenstein projective (resp., injective) modules whenever m ≠ n, and the homological behavior of n-strongly Gorenstein projective (resp., injective) modules. We introduce the notion of n-strongly Gorenstein flat modules. Then we study the homological behavior of n-strongly Gorenstein flat modules, and the relation between these modules and n-strongly Gorenstein projective (resp., injective) modules. 相似文献
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G. A. Garkusha 《Journal of Mathematical Sciences》2002,112(3):4303-4312
The classes of FP-injective and weakly quasi-Frobenius rings are investigated. The properties of both classes of rings are closely related to the embedding of finitely presented modules in fp-flat and free modules, respectively. Using these properties, we characterize the classes of coherent CF- and FGF-rings. Moreover, it is proved that the group ring R(G) is FP-injective (weakly quasi-Frobenius, respectively) if and only if the ring R is FP-injective (weakly quasi-Frobenius) and G is locally finite. Bibliography: 15 titles. 相似文献
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《代数通讯》2013,41(11):4415-4432
Abstract Let R be a commutative Noetherian ring. There are several characterizations of Gorenstein rings in terms of classical homological dimensions of their modules. In this paper, we use Gorenstein dimensions (Gorenstein injective and Gorenstein flat dimension) to describe Gorenstein rings. Moreover a characterization of Gorenstein injective (resp. Gorenstein flat) modules over Gorenstein rings is given in terms of their Gorenstein flat (resp. Gorenstein injective) resolutions. 相似文献
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Let (C,E,s) be an extriangulated category with a proper class ξ of E-triangles.We study complete cohomology of objects in (C,E,s) by applying ξ-projective resolutions and ξ-injective coresolutions constructed in (C,E,s).Vanishing of complete cohomology detects objects with finite ξ-projective dimension and finite ξ-injective dimension.As a consequence,we obtain some criteria for the validity of the Wakamatsu tilting conjecture and give a necessary and sufficient condition for a virtually Gorenstein algebra to be Gorenstein.Moreover,we give a general technique for computing complete cohomology of objects with finite ξ-Gprojective dimension.As an application,the relations between ξ-projective dimension and ξ-Gprojective dimension for objects in (C,E,s) are given. 相似文献
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Let R be a ring, n a fixed nonnegative integer and FP
n
(F
n
) the class of all left (right) R-modules of FP-injective (flat) dimensions at most n. A left R-module M (resp., right R-module F) is called n-FI-injective (resp., n-FI-flat) if Ext
1(N,M) = 0 (resp., Tor
1(F,N) = 0) for any N ∈ FP
n
. It is shown that a left R-module M over any ring R is n-FI-injective if and only if M is a kernel of an FP
n
-precover f: A → B with A injective. For a left coherent ring R, it is proven that a finitely presented right R-module M is n-FI-flat if and only if M is a cokernel of an F
n
-preenvelope K → F of a right R-module K with F projective if and only if M ∈⊥
F
n
. These classes of modules are used to construct cotorsion theories and to characterize the global dimension of a ring. 相似文献