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右IF-环及凝聚环的挠理论 总被引:2,自引:0,他引:2
本文研究了右IF-环的性质,证明出环R是右IF-环当且仅当R是左凝聚环,并且是平坦模;由此证明出右IF-环与左GQF-环是等价的,其次应用右IF-环研究了凝聚环的挠理论性质,证明出凝聚环与T-凝聚环的关系。 相似文献
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右IF-环及凝聚环的挠理论 总被引:2,自引:0,他引:2
本文研究了右IF-环的性质,证明出环R是右IF-环当且仅当R是左凝聚环,并且是平坦模;由此证明出右IF-环与左GQF-环是等价的,其次应用右IF-环研究了凝聚环的挠理论性质,证明出凝聚环与T-凝聚环的关系。 相似文献
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本文证明了对有限群分次环R而言,下列条件等价:(1)R是左gr-自内射环(左gr-PF环,左gr-QF环,左gr-线性紧环).(2)R是左自内射环(左PF环,左QF环,左线性紧环).(3)R#G*是左自内射环(左PF环,左QF环,左线性紧环). 相似文献
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关于半交换环与强正则环 总被引:1,自引:0,他引:1
本文得到了环R是强正则环的若干充分必要条件,证明了下面条件是等价的:(1)R是强正则的;(2)R是半交换正则的;(3)R是半交换的左SF-环;(4)R是半交换的ELT环,且使得每个单左R-模是P-内射的或者平坦的;(5)R是半交换右非奇异的左SF-环;(6)R是半素的半交换左(或右)P-内射环. 相似文献
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本文中我们引进强几乎优越扩张的概念并证明了若S≥R是(强几乎)优越扩张,则S是右Ⅱ-凝聚环当且仅当R是右Ⅱ-凝聚环。 相似文献
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本文主要证明了(1)当G是有限群时,G-型分次环R是gr-正则的当且仅当RG是正则的当且仅当M_G(R)是gr-正则的当且仅当对每个和G的任意非空子集H和F,M_(HXF)(R)的每个矩阵都有1-逆。(2)当G是任意群,G-型分次环只是反gr-正则的当且仅当F是反正则的当且仅当对每个和G的任意作非空子集H和K,FM_(H×F)(R)的每个矩阵有2-逆当且仅当FM_G(R)是gr-反正则的。 相似文献
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A ring R is called left morphic, if for any a ∈ R, there exists b ∈ R such that 1R(a) = Rb and 1R(b) = Ra. In this paper, we use the method which is different from that of Lee and Zhou to investigate when R[x, σ]/(xn) is (left) morphic and when the ideal extension E(R, V) is (left) morphic. It is mainly shown that: (1) If σis an automorphism of a division ring R, then S = R[x,σ]/(xn) (n > 1) is a special ring. (2) If d, m are positive integers and n = dm, then E(/n, mZn) is a morphic ring if and only if gcd(d, m) = 1. 相似文献
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本文介绍了强clean—般环的概念并将一些基本的结果推广到这个更广的环类.证明了强clean一般环的角落环和强π-正则一般环都是强clean的,还讨论了强clean一般环的扩张并且证明了满足条件J(I)=Q(I)的交换clean一般环的上三角矩阵环是强clean的. 相似文献
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为了统一交换环和约化环的层表示,Lambek引进了Symmetric环.继续symmetric环的研究,定义引入了强symmetric环的概念,研究它的一些扩张性质.证明环R是强symmetric环当且仅当R[x]是强symmetric环当且仅当R[x;x~(-1)]是强symmetric环.也证明对于右Ore环R的经典右商环Q,R是强symmetric环当且仅当Q是强symmetric环. 相似文献
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We in this note introduce a new concept, so called strongly J-semiclean ring, that is a generalization of strongly J-clean rings. We first observe the basic properties of strongly J-semiclean rings, constructing typical examples. We next investigate conditions on a local ring R that imply that the upper triangular matrix ring T_n(R) is a strongly J-semiclean ring. Also,the criteria on strong J-semicleanness of 2 × 2 matrices in terms of a quadratic equation are given. As a consequence, several known results relating to strongly J-clean rings are extended to a more general setting. 相似文献
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Let R be a ring and I an ideal of R.A ring R is called I-semi-π-regular if R/I isπ-regular and idempotents of R can be strongly lifted modulo I.Charac- terizations of I-semi-π-regular rings are given and relations between semi-π-regular rings and semiregular rings are explored. 相似文献
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