排序方式: 共有18条查询结果,搜索用时 15 毫秒
11.
Let R be a ring. M is said to be a minannihilator left R-module if r M l R (I) = IM for any simple right ideal I of R. A right R-module N is called simple-flat if Nl R (I) = l N (I) for any simple right ideal I of R. R is said to be a left simple-Baer (resp., left simple-coherent) ring if the left annihilator of every simple right ideal is a direct summand of R R (resp., finitely generated). We first obtain some properties of minannihilator and simple-flat modules. Then we characterize simple-coherent rings, simple-Baer rings, and universally mininjective rings using minannihilator and simple-flat modules. 相似文献
12.
Qun-xing Pan 《代数通讯》2013,41(10):3955-3973
Let H be a Hopf algebra and A an H-bimodule algebra. This article investigates homological dimensions and Gorenstein dimensions of L-R smash products A?H. Several well-known results are generalized. Moreover, we explore the stability of Gorenstein projective (flat) precovers and Gorenstein injective preenvelopes between the category of left A-modules and the category of left A?H-modules. 相似文献
13.
A left R-module M is called strongly P-projective if Exti(M, P) = 0 for all projective left R-modules P and all i ≥ 1. In this article, we first discuss properties of strongly P-projective modules. Then we introduce and study the strongly P-projective dimensions of modules and rings. The relations between the strongly P-projective dimension and other homological dimensions are also investigated. 相似文献
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15.
Let C be a semidualizing module for a commutative ring R. In this paper, we study the resulting modules of finite G C -projective dimension in Bass class, showing that they admit G C -projective precover. Over local ring, we prove that dim R (M) ≤ 𝒢? C ? id R (M) for any nonzero finitely generated R-module M, which generalizes a result due to Bass. 相似文献
16.
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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In this article, the concept of Gorenstein FP-injective modules and some related known results are generalized to Gorenstein FP-injective complexes. Moreover, some new characterizations of Gorenstein flat complexes are given. It is also proved that every complex has a Gorenstein flat preenvelope over coherent rings with finite self-FP-injective dimension. 相似文献
18.
Septimiu Crivei 《代数通讯》2013,41(2):529-545
We introduce generalizations of extending modules and lifting modules relative to proper classes of short exact sequences of modules, and we characterize modules for which any direct sums of copies of them are such relative extending modules or relative lifting modules. 相似文献