共查询到19条相似文献,搜索用时 62 毫秒
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关于周期环与Jacobson环的几个定理 总被引:2,自引:1,他引:2
A ring R is called a periodic ring, if for every x∈R there exist two distinct positive integers m(x) and n(x) such that xm(x)=xn(x)(cf. [1]), in particularly, if m(x) = 1 for any x∈R. then this periodic ring is called a Jacobson ring (cf. [2]).In this paper, a necessary and sufficient condition for a ring to be a Jacobson ring is given and some necessary and sufficient conditions for a periodic ring or a Jacobson ring to be a field are also given. 相似文献
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YoshiZawa型周期解定理和Massera型周期解定理研究进展简介 总被引:4,自引:0,他引:4
微分方程解的有界性和周期解的存在性是檄分方程理论研究中的两个重要课题,二者之间有着紧密的联系.在解的有界性与周期解的存在性的研究中,Yoshizawa周期解定理和Massera周期解定理是非常重要的结果,具有重要的理论意义和应用价值.本文以Yoshizawa型周期解定理和Massera型周期解定理的研究为主,简要介绍泛函微分方程周期解理论研究方面的一些新进展。 相似文献
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设R和T是Noether完备半局部环,R→T是环同态.本文证明了,若T是有限生成或ArtinR-模,M为G-Matlis自反R-模,则对所有n≥0,ExtRn(T,M),ExtRn(M,T),TorRn(T,M)以及TorRn(M,T)均是G-Matlis自反T-模.所得结果推广了R.Belshof的结果. 相似文献
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岳宏志 《纯粹数学与应用数学》1993,9(1):100-104
我们考虑如下微分系统:其中X∈R~n,f关于(t,X)连续且保证解的存在唯一性,f(t+T,X)=f(t.X)(T>0) 再考虑(1)的特例(2): 相似文献
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Shushi Harashita 《代数通讯》2013,41(4):1282-1290
In this article, for a noncommutative ring A with some rich structure, we define a ring of Witt vectors with coefficients in A, which is noncommutative unless A is commutative. 相似文献
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FP—内射环和IF环的几个特征 总被引:2,自引:1,他引:2
本文给出了FP—内射环和IF环的如下几个特征:(l)R为右FP—内射环当且仅当任意左R—模正合列Kn→Kn→N→0 N为无挠模,当且仅当任一n阶矩阵环为右P—内射环;(2)R为左IF环当且仅当任一有限生成左R—模均可嵌入平坦模;(3)R为IF环当且仅当R为伪凝聚的上平坦环。 相似文献
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In this paper,we introduced the concept of FA,δ-ring and the concept of generalized periodic ring, the structure theorems for some FA,δ-rings and generalized periodic rings are given. 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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C. Jayaram 《代数通讯》2013,41(1):206-212
In this article we establish some characterizations for Dedekind rings. 相似文献
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G. S. Suleimanova 《Acta Appl Math》2005,85(1-3):291-296
For a commutative ring K the conception of a strongly maximal ideal J was introduced by Kuzucuoglu and Levchuk in 2000. Denote by Rn(K,J) the ring of all n×n-matrices over K with elements from J on and above the main diagonal. Recent results on ideals of the ring Rn(K,J) for this case, ideals of the associated Lie ring and normal subgroups of the adjoint group are considered in this paper. Also ideals of Rn(K,J) for the case of an arbitrary associative ring K with the identity are investigated. 相似文献
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J-semicommutative环的性质 总被引:1,自引:0,他引:1
环冗称为J—semicommutative若对任意B,b∈R由ab=0可以推得aRb∈J(R),这里J(R)是环R的Jacobson根.环R是J—semicommutative环当且仅当它的平凡扩张是J—semicommutative环当且仅当它的Don'oh扩张是J—semicommutative环当且仅当它的Nagata扩张是,一semicommutative环当且仅当它的幂级数环是J—semicommutative环.若R/J(R)是semicommutative环,则可得到R是J-semicommutative环.本文进一步论证了如果,是环月的一个幂零理想,且R/I是J—semicommutative环,则R也是J-semicommutative环最后给出了J—semicommutative环与其他一些常见环的联系 相似文献