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Let R be any ring. A right R-module M is called n-copure projective if Ext1(M, N) = 0 for any right R-module N with fd(N) ≤ n, and M is said to be strongly copure projective if Ext i (M, F) = 0 for all flat right R-modules F and all i ≥ 1. In this article, firstly, we present some general properties of n-copure projective modules and strongly copure projective modules. Then we define and investigate copure projective dimensions of modules and rings. Finally, more properties and applications of n-copure projective modules, strongly copure projective modules and copure projective dimensions are given over coherent rings with finite self-FP-injective dimension. 相似文献
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Let R be a left coherent ring. We first prove that a right R-module M is strongly copure flat if and only if Ext i (M, C) = 0 for all flat cotorsion right R-modules C and i ≥ 1. Then we define and investigate copure flat dimensions of left coherent rings. Finally, we give some new characterizations of n-FC rings. 相似文献
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Zenghui Gao 《代数通讯》2013,41(8):3035-3044
This article continues to investigate a particular case of Gorenstein FP-injective modules, called strongly Gorenstein FP-injective modules. Some examples are given to show that strongly Gorenstein FP-injective modules lie strictly between FP-injective modules and Gorenstein FP-injective modules. Various results are developed, many extending known results in [1]. We also characterize FC rings in terms of strongly Gorenstein FP-injective, projective, and flat modules. 相似文献
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In this article, we study the weak global dimension of coherent rings in terms of the left FP-injective resolutions of modules. Let R be a left coherent ring and ? ? the class of all FP-injective left R-modules. It is shown that wD(R) ≤ n (n ≥ 1) if and only if every nth ? ?-syzygy of a left R-module is FP-injective; and wD(R) ≤ n (n ≥ 2) if and only if every (n ? 2)th ? ?-syzygy in a minimal ? ?-resolution of a left R-module has an FP-injective cover with the unique mapping property. Some results for the weak global dimension of commutative coherent rings are also given. 相似文献
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We study the existence of covers and envelopes by some special functors on the category of finitely presented modules. As an application, we characterize some important rings using these functors. We also investigate homological properties of some functors on the stable module category. The relationship between phantoms and Ext-phantoms is obtained. It is shown that every left R-module M has an Ext-phantom preenvelope f: M → N with coker(f) pure-projective. Finally, we prove that, as a torsionfree class of (mod-R, Ab), (mod-R, Ab) is generated by the FP-injective objects. 相似文献
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In this article, Gorenstein FP-injective modules are introduced and investigated. A left R-module M is called Gorenstein FP-injective if there is an exact sequence … → E 1 → E 0 → E 0 → E 1 → … of FP-injective left R-modules with M = ker(E 0 → E 1) such that Hom R (P, ?) leaves the sequence exact whenever P is a finitely presented left R-module with pd R (P) < ∞. Some properties of Gorenstein FP-injective modules are obtained. Several well-known classes of rings are characterized in terms of Gorenstein FP-injective modules. 相似文献
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A ring R is called left P-coherent in case each principal left ideal of R is finitely presented. A left R-module M (resp. right R-module N) is called D-injective (resp. D-flat) if Ext1(G, M) = 0 (resp. Tor1(N, G) = 0) for every divisible left R-module G. It is shown that every left R-module over a left P-coherent ring R has a divisible cover; a left R-module M is D-injective if and only if M is the kernel of a divisible precover A → B with A injective; a finitely presented right R-module L over a left P-coherent ring R is D-flat if and only if L is the cokernel of a torsionfree preenvelope K → F with F flat. We also study the divisible and torsionfree dimensions of modules and rings. As applications, some new characterizations of von Neumann regular rings and PP rings are given. 相似文献
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A module M is called strongly FP-injective if Exti(P,M) = 0 for any finitely presented module P and all i≥1. (Pre)envelopes and (pre)covers by strongly FP-injective modules are studied. We also use these modules to characterize coherent rings. An example is given to show that (strongly) FP-injective (pre)covers may fail to be exist in general. We also give an example of a module that is FP-injective but not strongly FP-injective. 相似文献
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Let R be a commutative ring. We investigate the relationship between (pre)covers ((pre)envelopes) of an R-module and the counterparts of the corresponding homomorphism module or tensor product module. Some applications are also given. 相似文献
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In the Gorenstein homological theory, Gorenstein projective and Gorenstein injective dimensions play an important and fundamental role. In this paper, we aim at studying the closely related strongly Gorenstein flat and Gorenstein FP-injective dimensions, and show that some characterizations similar to Gorenstein homological dimensions hold for these two dimensions. 相似文献
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This article studies characterizing local rings in terms of homological dimensions. The key tool is the notion of a prethick subcategory which we introduce in this article. Our methods recover the theorems of Salarian, Sather-Wagstaff, and Yassemi. 相似文献
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In this article, we investigate when every simple module has a projective (pre)envelope. It is proven that (1) every simple right R-module has a projective preenvelope if and only if the left annihilator of every maximal right ideal of R is finitely generated; (2) every simple right R-module has an epic projective envelope if and only if R is a right PS ring; (3) Every simple right R-module has a monic projective preenvelope if and only if R is a right Kasch ring and the left annihilator of every maximal right ideal of R is finitely generated. 相似文献