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众所周知,Assem-SmalΦ定理在倾斜理论中有重要的作用.本文的目的是建立一个在余模范畴中的Assem-SmalΦ定理的版本,并通过利用预包络理论来刻画余模范畴中的余倾斜挠类. 相似文献
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In this article, we first study the existence of envelopes and covers by modules of finite divisible and torsionfree dimensions. Then we investigate divisible and torsionfree dimensions as well as localizations of divisible and torsionfree modules over commutative rings. Finally, Gorenstein divisible and torsionfree modules are introduced and studied. 相似文献
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Let R be a ring and 𝒲 a self-orthogonal class of left R-modules which is closed under finite direct sums and direct summands. A complex C of left R-modules is called a 𝒲-complex if it is exact with each cycle Z n (C) ∈ 𝒲. The class of such complexes is denoted by 𝒞𝒲. A complex C is called completely 𝒲-resolved if there exists an exact sequence of complexes D · = … → D ?1 → D 0 → D 1 → … with each term D i in 𝒞𝒲 such that C = ker(D 0 → D 1) and D · is both Hom(𝒞𝒲, ?) and Hom(?, 𝒞𝒲) exact. In this article, we show that C = … → C ?1 → C 0 → C 1 → … is a completely 𝒲-resolved complex if and only if C n is a completely 𝒲-resolved module for all n ∈ ?. Some known results are obtained as corollaries. 相似文献
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In this article, some new characterizations of Gorenstein projective, injective, and flat modules over commutative noetherian local rings are given. 相似文献
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Let M R be a right R-module over a ring R with S = End(M R ). We study the coherence of the left S-module S M relative to a hereditary torsion theory for the category of right R-modules. Various results are developed, many extending known results. 相似文献
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The authors introduce and investigate the Tc-Gorenstein projective, Lc- Gorenstein injective and Hc-Gorenstein flat modules with respect to a semidualizing module C which shares the common properties with the Gorenstein projective, injective and flat modules, respectively. The authors prove that the classes of all the Tc-Gorenstein projective or the Hc-Gorenstein flat modules are exactly those Gorenstein projective or flat modules which are in the Auslander class with respect to C, respectively, and the classes of all the Lc-Gorenstein 'injective modules are exactly those Gorenstein injective modules which are in the Bass class, so the authors get the relations between the Gorenstein projective, injective or flat modules and the C-Gorenstein projective, injective or flat modules. Moreover, the authors consider the Tc(R)-projective and Lc(R)-injective dimensions and Tc(R)-precovers and Lc(R)-preenvelopes. Fiually, the authors study the Hc-Gorenstein flat modules and extend the Foxby equivalences. 相似文献