共查询到20条相似文献,搜索用时 15 毫秒
1.
Given a positive integer n, a left R-module M is called n-coherent (resp. n-semihereditary) if every n-generated submodule of M is finitely presented (resp. projective). We investigate the properties of n-coherent modules and n-semihereditary modules. Various results are developed, many extending known results. 相似文献
2.
A right R-module M is called glat if any homomorphism from any finitely presented right R-module to M factors through a finitely presented Gorenstein projective right R-module. The concept of glat modules may be viewed as another Gorenstein analogue of flat modules. We first prove that the class of glat right R-modules is closed under direct sums, direct limits, pure quotients and pure submodules for arbitrary ring R. Then we obtain that a right R-module M is glat if and only if M is a direct limit of finitely presented Gorenstein projective right R-modules. In addition, we explore the relationships between glat modules and Gorenstein flat (Gorenstein projective) modules. Finally we investigate the existence of preenvelopes and precovers by glat and finitely presented Gorenstein projective modules. 相似文献
3.
Li-Xin Mao 《Proceedings Mathematical Sciences》2008,118(4):557-567
A ring is called right P-coherent if every principal right ideal is finitely presented. Let M
R
be a right R-module. We study the P-coherence of the endomorphism ring S of M
R
. It is shown that S is a right P-coherent ring if and only if every endomorphism of M
R
has a pseudokernel in add M
R
; S is a left P-coherent ring if and only if every endomorphism of M
R
has a pseudocokernel in add M
R
. Some applications are given. 相似文献
4.
Ladislav Bican 《Mathematica Slovaca》2007,57(4):333-338
In this note we are going to show that if M is a left module over a left noetherian ring R of the infinite cardinality λ ≥ |R|, then its injective hull E(M) is of the same size. Further, if M is an injective module with |M| ≥ (2λ)+ and K ≤ M is its submodule such that |M/K| ≤ λ, then K contains an injective submodule L with |M/L| ≤ 2λ. These results are applied to modules which are torsionfree with respect to a given hereditary torsion theory and generalize
the results obtained by different methods in author’s previous papers: [A note on pure subgroups, Contributions to General Algebra 12. Proceedings of the Vienna Conference, June 3–6, 1999, Verlag Johannes Heyn, Klagenfurt,
2000, pp. 105–107], [Pure subgroups, Math. Bohem. 126 (2001), 649–652].
This research has been partially supported by the Grant Agency of the Charles University, grant #GAUK 301-10/203115/B-MAT/MFF
and also by the institutional grant MSM 113 200 007. 相似文献
5.
A. A. Tuganbaev 《Mathematical Notes》1999,65(6):739-748
This paper continues the study of Noetherian serial rings. General theorems describing the structure of such rings are proved. In particular, some results concerning π-projective and π-injective modules over serial rings are obtained. Translated fromMatematicheskie Zametki, Vol. 65, No. 6, pp. 880–892 June, 1999. 相似文献
6.
Yuedi Zeng 《代数通讯》2018,46(11):4941-4953
A ring R is called left slightly P-coherent if C is P-injective, for every left R-module exact sequence 0→A→B→C→0 with A and B P-injective. The properties of slightly P-coherent rings and several examples are studied to show that left slightly P-coherent rings fall in between left P-coherent rings and left strongly P-coherent rings. In terms of some derived functors, some homological dimensions over these rings are investigated. As applications, some new characterizations of p.p.rings are given. 相似文献
7.
Guocheng Dai 《代数通讯》2018,46(3):1267-1271
In this paper, we prove that a ring R is left coherent if and only if the class 𝒜bs of absolutely pure left R-modules is a covering class. 相似文献
8.
We investigate certain finite subgroups of , where is a finite nilpotent group. Such a group gives rise to a -module; we study the characters of these modules to limit the structure of . We also exhibit some exotic subgroups .
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D. J. Benson 《Algebras and Representation Theory》1999,2(3):287-294
Let k be a commutative ring of coefficients and G be a finite group. Does there exist a flat k G-module which is projective as a k-module but not as a k G-module? We relate this question to the question of existence of a k-module which is flat and periodic but not projective. For either question to have a positive answer, it is at least necessary to have |k| ≥ ?ω. There can be no such example if k is Noetherian of finite Krull dimension, or if k is perfect. 相似文献
13.
F. Wehrung 《代数通讯》2013,41(12):5893-5919
We extend the usual definition of coherence, for modules over rings, to partially ordered right modules over a large class of partially ordered rings, called po-rings. In this situation, coherence is equivalent to saying that solution sets of finite systems of inequalities are finitely generated semimodules. Coherence for ordered rings and modules, which we call po-coherence, has the following features:. (i) Every subring of Q, and every totally ordered division ring, is po-coherent. (ii) For a partially ordered right module Aover a po-coherent poring R Ais po-coherent if and only if Ais a finitely presented .R-module and A +is a finitely generated R +-semimodule. (iii) Every finitely po-presented partially ordered right module over a right po-coherent po-ring is po-coherent. (iv) Every finitely po-presented abelian lattice-ordered group is po-coherent. 相似文献
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Bo Lu 《数学研究通讯:英文版》2016,32(4):339-351
In this article, we introduce and study the concept of n-Gorenstein injective(resp., n-Gorenstein flat) modules as a nontrivial generalization of Gorenstein injective(resp., Gorenstein flat) modules. We investigate the properties of these modules in various ways. For example, we show that the class of n-Gorenstein injective(resp., n-Gorenstein flat) modules is closed under direct sums and direct products for n ≥ 2. To this end, we first introduce and study the notions of n-injective modules and n-flat modules. 相似文献
16.
Robert L. Snider 《Proceedings of the American Mathematical Society》1996,124(4):1043-1049
If is a finitely generated nilpotent group which is not abelian-by-finite, a field, and a finite dimensional separable division algebra over , then there exists a simple module for the group ring with endomorphism ring . An example is given to show that this cannot be extended to polycyclic groups.
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It is proved that is injective if is an injective module over a valuation ring , for each prime ideal . Moreover, if or is flat, then is injective, too. It follows that localizations of injective modules over h-local Prüfer domains are injective, too.
19.
约化环和半交换环 总被引:1,自引:0,他引:1
张春霞 《纯粹数学与应用数学》2008,24(1):121-124
讨论了在约化条件下,比平凡扩张更广泛的一类扩张环的半交换性.通过给出半交换模的定义,得到平凡扩张是半交换环的一个充要条件. 相似文献
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