共查询到20条相似文献,搜索用时 15 毫秒
1.
M. Jayaraman 《代数通讯》2013,41(11):3331-3345
We study generalizations of regular modules by Ramamurthy and Mabuchi. These are also generalizations of fully right idempotent and fully left idempotent rings, respectively. We also define and study the properties of *-weakly regular modules, a generalization of fully idempotent rings. 相似文献
2.
Abelian正则环的零因子图 总被引:4,自引:0,他引:4
We introduce the zero-divisor graph for an abelian regular ring and show that if R, S are abelian regular, then (K0(R),[R])≌(K0(S),[S])if and only if they have isomorphic reduced zero-divisor graphs. It is shown that the maximal right quotient ring of a potent semiprimitive normal ring is abelian regular,moreover,the zero-divisor graph of such a ring is studied. 相似文献
3.
本文分别讨论了关于结合环和半群的二个定理,并且由结合环的这二个定理推出了如下准则:结合环R是Abel正则的,当且仅当R的每个拟理想是正则环. 相似文献
4.
本文证明了任意环的整体Ding投射维数和整体Ding内射维数一致,研究了奇点范畴和相对于Ding模的稳定范畴间的关系,并刻画了Gorenstein (正则)环以及环的整体维数的有限性. 相似文献
5.
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
6.
Let C be an Abelian group. An Abelian group A in some class
of Abelian groups is said to be
C
H-definable in the class
if, for any group B\in
, it follows from the existence of an isomorphism Hom(C,A) Hom(C,B) that there is an isomorphism A B. If every group in
is
C
H-definable in
, then the class
is called an
C
H-class. In the paper, conditions are studied under which a class of completely decomposable torsion-free Abelian groups is a
C
H-class, where C is a completely decomposable torsion-free Abelian group. 相似文献
7.
8.
E. V. Sokolov 《Mathematical Notes》2005,78(5-6):696-708
It is proved that an arbitrary descending HNN-extension of a finitely generated Abelian group is conjugacy separable. 相似文献
9.
Tao Xu & Heguo Liu 《数学研究通讯:英文版》2016,32(2):167-172
Let G be a finitely generated torsion-free nilpotent group and α an automorphism of prime order p of G. If the map φ : G-→ G defined by gφ= [g, α]is surjective, then the nilpotent class of G is at most h(p), where h(p) is a function depending only on p. In particular, if α3= 1, then the nilpotent class of G is at most2. 相似文献
10.
本文用则模的术语给出了半单Artin 环的刻划。得到如下三个条件的等价性:(1)R 是一个半单Artin 环;(2)每一个R-模都是正则模;(3)每一个单纯R-模都是正则模。 相似文献
11.
A finite group G is called a Schur group, if any Schur ring over G is associated in a natural way with a subgroup of Sym(G) that contains all right translations. Recently, the authors have completely identified the cyclic Schur groups. In this article, it is shown that any abelian Schur group belongs to one of several explicitly given families only. In particular, any noncyclic abelian Schur group of odd order is isomorphic to ?3 × ?3 k or ?3 × ?3 × ? p where k ≥ 1 and p is a prime. In addition, we prove that ?2 × ?2 × ? p is a Schur group for every prime p. 相似文献
12.
文献 [1]中 ,Ming.R.Y.C引进了 YJ 内射模的概念 ,且指出正则环上的每个模均是 YJ 内射模 ,那么反之如何呢 ?文 [1]中做了一些结果 ,本文拟就这个问题作进一步讨论 . 相似文献
13.
14.
17.
群分次环与群分次模的基座 总被引:1,自引:0,他引:1
将关于交叉积的基座的主要结果推广到了群分次环上,得到了群分次环的基座的一些具体刻划,特别地,证明了对有限群G和强G-分次环R,有Soc(RR) Soc(ReRe)R soc^ |G|(RR)。 相似文献
18.
A right module M over a ring R is called feebly Baer if, whenever xa = 0 with x ∈ M and a ∈ R, there exists e2 = e ∈ R such that xe = 0 and ea = a. The ring R is called feebly Baer if RR is a feebly Baer module. These notions are motivated by the commutative analog discussed in a recent paper by Knox, Levy, McGovern, and Shapiro [6]. Basic properties of feebly Baer rings and modules are proved, and their connections with von Neumann regular rings are addressed. 相似文献
19.
Glaz and Wickless introduced the class G of mixed abelian groups A which have finite torsion-free rank and satisfy the following three properties: i) A
p is finite for all primes p, ii) A is isomorphic to a pure subgroup of
P
A
P and iii) Hom(A, tA) is torsion. A ring R is a left Kasch ring if every proper right ideal of R has a non-zero left annihilator. We characterize the elements A of G such that E(A)/tE(A) is a left Kasch ring, and discuss related results. 相似文献
20.
R. R. Andruszkiewicz 《代数通讯》2013,41(9):3760-3767
An abelian group is called a mixed one if it is neither torsion nor torsion-free. It is to be proved that every mixed group can be provided with a nonzero associative ring structure. Our methods of proofs are straightforward and elementary. 相似文献