共查询到18条相似文献,搜索用时 93 毫秒
1.
《数学研究及应用》2016,(4)
A ring R is said to be π-semicommutative if a, b ∈ R satisfy ab = 0 then there exists a positive integer n such that anRbn= 0. We study the properties of π-semicommutative rings and the relationship between such rings and other related rings. In particular, we answer a question on left GWZI rings negatively. 相似文献
2.
Xiao Bin YIN Rui WANG Xiao Long LI College of Mathematics Computer Science Anhui Normal University Anhui P.R.China 《数学研究与评论》2011,(6)
In this paper,we introduce a non-trivial generalization of ZI-rings-quasi ZI-rings.A ring R is called a quasi ZI-ring,if for any non-zero elements a,b ∈ R,ab = 0 implies that there exists a positive integer n such that an = 0 and anRbn = 0.The non-singularity and regularity of quasi ZI,GP-Vˊ-rings are studied.Some new characterizations of strong regular rings are obtained.These effectively extend some known results. 相似文献
3.
As generalization of r-clean rings and weakly clean rings, we define a ring R is weakly r-clean if for any a∈R there exist an idempotent e and a regular element r such that a = r + e or a = r-e. Some properties and examples of weakly r-clean rings are given. Furthermore, we prove the weakly clean rings and weakly r-clean rings are equivalent for abelian rings. 相似文献
4.
Let R be a ring. A fight R-module M is called f-projective if Ext^1 (M, N) = 0 for any f-injective right R-module N. We prove that (F-proj,F-inj) is a complete cotorsion theory, where (F-proj (F-inj) denotes the class of all f-projective (f-injective) right R-modules. Semihereditary rings, von Neumann regular rings and coherent rings are characterized in terms of f-projective modules and f-injective modules. 相似文献
5.
Let R be a ring and J(R) the Jacobson radical. An element a of R is called(strongly) J-clean if there is an idempotent e ∈ R and w ∈ J(R) such that a = e + w(and ew = we). The ring R is called a(strongly) J-clean ring provided that every one of its elements is(strongly) J-clean. We discuss, in the present paper,some properties of J-clean rings and strongly J-clean rings. Moreover, we investigate J-cleanness and strongly J-cleanness of generalized matrix rings. Some known results are also extended. 相似文献
6.
A ring R is said to be weakly semicommutative if for any a,b∈R, ab=0 implies aRb(?)Nil(R),where Nil(R) is the set of all nilpotent elements in R. In this note,we clarify the relationship between weakly semicommutative rings and NI-rings by proving that the notion of a weakly semicommutative ring is a proper generalization of NI-rings.We say that a ring R is weakly 2-primal if the set of nilpotent elements in R coincides with its Levitzki radical,and prove that if R is a weakly 2-primal ring which satisfiesα-condition for an endomorphismαof R(that is,ab=0(?)aα(b)=0 where a,b∈R) then the skew polynomial ring R[x;α] is a weakly 2-primal ring,and that if R is a ring and I is an ideal of R such that I and R/I are both weakly semicommutative then R is weakly semicommutative. Those extend the main results of Liang et al.2007(Taiwanese J.Math.,11(5)(2007), 1359-1368) considerably.Moreover,several new results about weakly semicommutative rings and NI-rings are included. 相似文献
7.
In this paper, we generalize flat modules, regular rings and V- rings to the situation of a hereditary torsion theory, that a ring R is regular if and only if R is a left nonsingular ring and for every essential left ideal o of R, and for eve ry element a∈o there exists a element a′∈o , such that a= aa′. (theorem 3.3). 相似文献
8.
Pseudopolar rings are closely related to strongly π-regular rings, uniquely strongly clean rings and semiregular rings. In this paper, we investigate pseudopolarity of generalized matrix rings K s(R) over a local ring R. We determine the conditions under which elements of K s(R) are pseudopolar. Assume that R is a local ring. It is shown that A ∈ K s(R) is pseudopolar if and only if A is invertible or A2∈ J(K s(R)) or A is similar to a diagonal matrix[u 00 j], where l u-r j and l j-r u are injective and u ∈ U(R) and j ∈ J(R). Furthermore, several equivalent conditions for K s(R)over a local ring R to be pseudopolar are obtained. 相似文献
9.
ZhiXiangWU 《数学学报(英文版)》2005,21(2):249-260
In this paper, we prove that R is a two-sided Artinian ring and J is a right annihilator ideal if and only if (i) for any nonzero right module, there is a nonzero linear map from it to a projective module; (ii) every submodule of RR is not a radical module for some right coherent rings. We call a ring a right X ring if Homa(M, R) = 0 for any right module M implies that M = 0. We can prove some left Goldie and right X rings are right Artinian rings. Moreover we characterize semisimple rings by using X rings. A famous Faith‘s conjecture is whether a semipimary PF ring is a QF ring. Similarly we study the relationship between X rings and QF and get many interesting results. 相似文献
10.
$GP$-$V^{''}$-环的非奇异性与正则性 总被引:1,自引:0,他引:1
In this paper,we introduce a non-trivial generalization of ZI-rings-quasi ZI-rings.A ring R is called a quasi ZI-ring,if for any non-zero elements a,b ∈ R,ab = 0 implies that there exists a positive integer n such that an = 0 and anRbn = 0.The non-singularity and regularity of quasi ZI,GP-Vˊ-rings are studied.Some new characterizations of strong regular rings are obtained.These effectively extend some known results. 相似文献
11.
研究了广义半交换环的幂零结构,定义了一类新的环类,即幂零$\alpha$-半交换环.说明了$\alpha$-半交换环与半交换环, $\alpha$-半交换环和$\alpha$-刚性环等环密切相关,通过构造反例说明了幂零$\alpha$-半交换环未必是$\alpha$-半交换环.研究了幂零$\alpha$-半交换环的各种性质,推广和统一了与环的半交换性质有关的若干结论. 相似文献
12.
本文引进左(右)零因子环的概念,它们是一类无单位元的环.我们称一个环为左(右)零因子环,如果对于任何 $a \in R$,都有$r_R (a) \neq 0~(l_R(a)\neq 0)$,而称一个环为强左(右)零因子环,如果$r_R(R)\neq 0~(l_R(R)\neq 0)$.Camillo和Nielson称一个环$R$为右有限零化环(简称RFA-环),如果$R$的每一个有限子集都有非零的右零化子.本文给出左零因子环的一些基本例子,探讨强左零因子环和RFA-环的扩张,并给出它们的等价刻画. 相似文献
13.
For a monoid M, we introduce the concept of skew strongly M-reversible rings which is a generalization of strongly M-reversible rings, and investigate their properties. It is shown that if G is a finitely generated Abelian group, then G is torsion-free if and only if there exists a ring R with |R| ≥ 2 such that R is skew strongly G-reversible. Moreover, we prove that if R is a right Ore ring with classical right quotient ring Q, then R is skew strongly M-reversible if and only if Q is skew strongly M-reversible. 相似文献
14.
15.
Masako Furuya Masataka Tomari 《Proceedings of the American Mathematical Society》2004,132(7):1885-1890
We give an inequality on the Milnor number of a hypersurface isolated singularity in terms of the weighted Taylor expansion for a given weight on the coordinates. Here the equality holds if and only if the leading term defines an isolated singularity. This gives a characterization of the semi-quasihomogeneous condition in terms of . Our proof uses a result on multiplicity of filtered rings and is given by purely algebraic arguments.
16.
In this paper, a generalization of the class of semicommutative rings is investigated.A ring R is called left GWZI if for any a ∈ R, l(a) is a GW-ideal of R. We prove that a ring R is left GWZI if and only if S3(R) is left GWZI if and only if Vn(R) is left GWZI for any n ≥ 2. 相似文献
17.
许扬 《数学年刊A辑(中文版)》2017,38(1):053-72
作者对非结合环给出扩展的概念,即给定2个非结合环A和B,对任一非结合环R,称R是A被B的扩展,当且仅当A是R的理想且R/A≌B.对非结合环的扩展,文中证明了一个类似于Schreier群扩张定理的结果.作为应用,对给定的自然数m≥2,n≥2,文章刻画了模n的剩余类环Z_n被模m的剩余类环Z_m扩展所得到的有限环R的构造,证明了R可以用满足一定条件的自然数对(u,r)来描述,同时写出了R的理想和单侧理想的具体形状.作者还进一步证明,R是结合的当且仅当R=Z_nZ_m,且当R=Z_nZ_m时,R的每个理想都是Z_n的一个理想与Z_m的一个理想的直和,即此时R的理想是相对平凡的. 相似文献
18.
本文研究了具有卷积的中心自反环的性质,定义并引入了中心-自反环,显然,中心-自反环是自反环、中心自反环和-自反环的推广.给出了这类环的一些特征,研究了相关的环扩张,包括平凡扩张,Dorroh扩张和多项式扩张. 相似文献