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环的Excellent扩张 总被引:12,自引:2,他引:10
设S是R的Excellent扩张.本文讨论了R的性质对S的影响及S的性质对R的影响,并利用所得结果改进和推广了一些已知的结论. 相似文献
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关于Heteroclinic环(包括Homoclinic环)的稳定性,目前仅有和在粗情况下的结果。对n=1时的临界情况有作者和钱敏的结果,而对其它情况,至今尚无法判定Heteroclimc环的稳定性。 本文对一般的临界情况给出了Heteroclinic环的稳定性判据,所得的结果包括并推广了作者和钱敏的原有结果并对这些结果给予统一的证明。 利用本文的主要结果,最后讨论了极限环的存在性及从Heteroclinic环分支出极限环的问题。 相似文献
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可换的广义正则环与广义 V 环的关系 总被引:3,自引:0,他引:3
本文把可换正则环类恰为可换 V 环类的结果推向广义的情形.定义了ι-正则环,并在可换情形研究它与文献[1]中提出的ι-V 环的关系. 相似文献
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Noether环理想的性质 总被引:1,自引:0,他引:1
Noether交换环是一类非常重要的环,本文主要对Noether交换环进行了研究和讨论,得到了Noether交换环、Noether整环的若干性质;并推广了文[1]中的部分结果. 相似文献
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临界情况下奇环的稳定性 总被引:11,自引:2,他引:9
关于确定奇环稳定性的问题,目前仅有А.А.Андронов和Л.А.Черкас在粗情况下分别对n=1及任意n的结果及作者和钱敏在临界情况下对n=1的结果。对其它情况问题至今尚未解决。 本文对临界情况及任意的n解决了这一问题。本文的结果包括了А.А.Андронов,Л.А.Черкас,作者和钱敏的三个老的结果并对这些结果给予统一的证明。 本文最后讨论了利用奇环的稳定性确定极限环的存在性及从奇环分支出极限环的问题。 相似文献
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Steve Szabo 《代数通讯》2019,47(3):1287-1298
In a paper on the taxonomy of 2-primal rings, examples of various types of rings that are related to commutativity such as reduced, symmetric, duo, reversible and PS I were given in order to show that the ring class inclusions were strict. Many of the rings given in the examples were infinite. In this paper, where possible, examples of minimal finite rings of the various types are given. Along with the rings in the previous taxonomy, NI, abelian and reflexive rings are also included. 相似文献
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《代数通讯》2013,41(11):5609-5625
Abstract The notion of semiclean elements in a ring is defined. Every clean element is semiclean. A ring R is said to be semiclean if every element in R is semiclean. The group ring Z p G with G a cyclic group of order 3 is proved to be semiclean. The n × n matrix ring M n (R) over a semiclean ring is semiclean. If R is a torsion free semiclean ring in which every element of R can be written as a sum of periodic and ±1, then R is clean. Every element in a semiclean ring R with 2 invertible is a sum of no more than 3 units. 相似文献
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Harpreet K. Grover 《代数通讯》2013,41(9):3288-3305
A ring R is said to be von Newmann local (VNL) if for any a ∈ R, either a or 1 ?a is (von Neumann) regular. The class of VNL rings lies properly between exchange rings and (von Neumann) regular rings. We characterize abelian VNL rings. We also characterize and classify arbitrary VNL rings without an infinite set of orthogonal idempotents; and also the VNL rings having a primitive idempotent e such that eRe is not a division ring. We prove that a semiperfect ring R is VNL if and only if for any right uni-modular row (a 1, a 2) ∈ R 2, one of the a i 's is regular in R. Formal triangular matrix rings that are VNL are also characterized. As a corollary, it is shown that an upper triangular matrix ring T n (R) is VNL if and only if n = 2 or 3 and R is a division ring. 相似文献
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Malcev-Neumann环的主拟Baer性质 总被引:2,自引:0,他引:2
设R是环,G是偏序群,σ是从G到R的自同构群的映射。本文研究了Malcev-Neumann环R*((G))是主拟Baer环的条件。证明了如下结果:如果R是约化环并且σ是弱刚性的,则R*((G))是主拟Baer环当且仅当R是主拟Baer环,并且I(R)的任意G可标子集在I(R)中具有广义并. 相似文献
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A ring R is called clean if every element of it is a sum of an idempotent and a unit. A ring R is neat if every proper homomorphic image of R is clean. When R is a field, then a complete characterization has been obtained for a commutative group ring RG to be neat, but not clean. And if R is not a field, then necessary conditions are obtained for a commutative group ring RG to be neat, but not clean. A counterexample is given to show that these necessary conditions are not sufficient. 相似文献
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In this paper we introduce and study the notion of a graded (strongly) nil clean ring which is group graded. We also deal with extensions of graded (strongly) nil clean rings to graded matrix rings and to graded group rings. The question of when nil cleanness of the component, which corresponds to the neutral element of a group, implies graded nil cleanness of the whole graded ring is examined. Similar question is discussed in the case of groupoid graded rings as well. 相似文献
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《Journal of Pure and Applied Algebra》2019,223(11):4583-4591
Marks showed that , the group algebra over the quaternion group, is a reversible nonsymmetric ring, then questioned whether or not this ring is minimal with respect to cardinality. In this work, it is shown that the cardinality of a minimal reversible nonsymmetric ring is indeed 256. Furthermore, it is shown that although is a duo ring, there are also examples of minimal reversible nonsymmetric rings which are nonduo. 相似文献
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E. Hashemi 《代数通讯》2013,41(3):1075-1083
For a monoid M, we introduce M-McCoy rings, which are a generalization of McCoy rings and M-Armendariz rings; and investigate their properties. We first show that all reversible rings are right M-McCoy, where M is a u.p.-monoid. We also show that all right duo rings are right M-McCoy, where M is a strictly totally ordered monoid. Then we show that semicommutative rings and 2-primal rings do have a property close to the M-McCoy condition. Moreover, it is shown that a finitely generated Abelian group G is torsion free if and only if there exists a ring R such that R is G-McCoy. Consequently, several known results on right McCoy rings are extended to a general setting. 相似文献
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The definition of AP-injectivity wnil-injectivity and almost nil n-injectivity motivates us to generalize the injectivity to almost The aim of this paper is to investigate characterizations and properties of almost wnil-injective rings and almost nil n-injective rings. Various results are developed, and many conclusions extend known results. 相似文献