共查询到20条相似文献,搜索用时 531 毫秒
1.
给出了伪投射模的另外一种等价定义,并对伪投射模的自同态环的Jacobson根做了讨论,还对伪投射盖做了某些探讨. 相似文献
2.
3.
4.
本文证明了若半Σ准投射模是弱n满投射的,则其自同态环的稳定秩至多为n,从而部分推广了文献[3]的—个主要结果. 相似文献
5.
6.
杜先能 《数学年刊A辑(中文版)》2006,(2)
本文研究形式三角矩阵环 R 的若干新性质,讨论 R-模的伪投射性,给出了形式三角矩阵环 R 是 V-环或半 V-环的充要条件.同时,给出了 R 是 PS-环的条件. 相似文献
7.
8.
刘永辉 《纯粹数学与应用数学》1997,13(2):124-128
引入了弱直投射和弱直内射模的概念,给出了它们的一些性质。使用弱直投射和弱直内射模刻划了遗传环、半遗传环、半单环和QF-环。 相似文献
9.
整环$R$被称为局部几乎完全整环, 指的是对任意极大理想${\frak m}$都有$R_{{\frak m}}$是几乎完全整环. 本文利用局部完全环, 几乎投射模, 弱内射模, 几乎强平坦模和强Matlis余挠模给出了局部几乎完全整环的若干等价刻画. 相似文献
10.
11.
We show that over a right coherent left perfect ring R, a complex C of left R-modules is Gorenstein projective if and only if C
m
is Gorenstein projective in R-Mod for all m ∈ ℤ. Basing on this we show that if R is a right coherent left perfect ring then Gpd(C) = sup{Gpd(C
m
)|m ∈ ℤ} where Gpd(−) denotes Gorenstein projective dimension. 相似文献
12.
This paper investigates the structure of cyclically pure (or C-pure) projective modules. In particular, it is shown that a ring R is left Noetherian if and only if every C-pure projective left R-module is pure projective. Also, over a left hereditary Noetherian ring R, a left R-module M is C-pure projective if and only if M = N ⊕ P, where N is a direct sum of cyclic modules and P is a projective left R-module. The relationship C-purity with purity and RD-purity are also studied. It is shown that if R is a local duo-ring, then the C-pure projective left R-modules and the pure projective left R-modules coincide if and only if R is a principal ideal ring. If R is a left perfect duo-ring, then the C-pure projective left R-modules and the pure projective left R-modules coincide if and only if R is left Köthe (i.e., every left R-module is a direct sum of cyclic modules). Also, it is shown that for a ring R, if every C-pure projective left R-module is RD-projective, then R is left Noetherian, every p-injective left R-module is injective and every p-flat right R-module is flat. Finally, it is shown that if R is a left p.p-ring and every C-pure projective left R-module is RD-projective, then R is left Noetherian hereditary. The converse is also true when R is commutative, but it does not hold in the noncommutative case. 相似文献
13.
Zuo Lancui 《大学数学》1998,(1)
本文研究了所有R—投射模都是投射模的环(RP—环),得出了它的几个等价条件,证明了:S=Rn为RP—环当且仅当R为RP—环;∑ni=1Ri为RP—环当且仅当每个Ri为RP—环.讨论了RP—环的左投射维数. 相似文献
14.
16.
In this article, several characterizations of certain classes of rings via FC-purity and I-purity are considered. Among others results, it is shown that every I-pure injective left R-module is projective if and only if every FC-pure projective left R-module is injective, if and only if, R is a semisimple ring. In particular, the structures of FC-pure projective and I-pure projective modules over a left Artinian ring are completely described. Also, it is shown that every left R-module is FC-pure projective if and only if every indecomposable left R-module is a finitely presented cyclic R-module, if and only if, R is a left Köthe ring. Finally, we introduce FC-pure flatness and I-pure flatness of modules and several characterizations of these notions are given. In particular, we show that a commutative ring R is quasi-Frobenius if and only if R is an Artinian ring and I-pure injective, if and only if, R is an Artinian ring and the injective envelope E(R) is an FC-pure projective R-module. 相似文献
17.
In this article, we study the characterizations of Gorenstein injective left S-modules and finitely generated Gorenstein projective left R-modules when there is a dualizing S-R-bimodule associated with a right noetherian ring R and a left noetherian ring S. 相似文献
18.
A. G. Gorinov 《Functional Analysis and Its Applications》2004,38(2):149-150
A problem posed by V. I. Arnold is solved by describing all homeomorphisms of an affine quaternion space that take any left or right affine quaternion line to a left or right affine quaternion line (a left line can be taken to a right one, and vice versa). 相似文献
19.
We analyze how the left perfect condition on a ring A (not necessarily with identity) relates to the left perfect condition on unital subrings of the form eAe (where e is idempotent). We then use this analysis to examine a class of graded left perfect rings. 相似文献