共查询到20条相似文献,搜索用时 78 毫秒
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通过引入环的幂等自反自同态α的概念,研究幂等自反α-环,它是幂等自反环概念的拓广.给出幂等自反α-环的一些特征和扩张性质,推广了已有的一些相关结果. 相似文献
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通过π-凝聚环上的f.g.模的自反性引进了WQF-环和GIF-环,给出了QF-环-个新的刻画,并研究了π-凝聚环上的W∧n模上的自反性的特征性质。 相似文献
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分次根、弱分次根与自反根 总被引:12,自引:0,他引:12
本文在一般群分次环范畴中,给出了典型分次根NG,LG,gG,rG和KG的元素刻划.通过建立弱分次根概念,研究了自反根Nref,Lref,gref,rref和Kref的性质,探讨了这些分次根和与它们相对应的自反根的关系. 相似文献
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本文研究了Abelπ-正则环的扩张.利用环的结构理论,证明了一个Abel环R(不必有1)是π-正则的当且仅当有理想I使得I和R/I都是π-正则的.推广了一些文献的结论. 相似文献
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GCD整环与自反模 总被引:3,自引:0,他引:3
王芳贵 《数学年刊A辑(中文版)》1994,(2)
本文证明了凝聚整环是GCD整环当且仅当秩为1的自反模是自由模.同时还得到有限弱整体维数的凝聚整环是GCD整环当且仅当Pic(R)=1.特别地,有限整体维数的Noether整环是UFD当且仅当Pic(R)=1. 相似文献
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A *-ring is called *-clean if every element of the ring can be written as the sum of a projection and a unit. For an integer n ≥ 1, we call a *-ring R n-*-clean if for any a ∈ R,a = p + u1 + ··· + unwhere p is a projection and ui are units for all i. Basic properties of n-*-clean rings are considered, and a number of illustrative examples of 2-*-clean rings which are not *-clean are provided. In addition, extension properties of n-*-clean rings are discussed. 相似文献
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A ring is said to be UR if every element can be written as the sum of a unit and a regular element. These rings are shown to be a unifying generalization of regular rings, clean rings and (S, 2)-ring~. Some relations of these rings are studied and several properties of clean rings and (S, 2)-rings are extended. PAng extensions of UR-rings are also investigated. 相似文献
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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
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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
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设$\delta$是一个$*$-代数$\mathcal A$到其左$\mathcal A$-模$\mathcal M$的可加映射, 如果对任意$A\in\mathcal A$, 有$\delta(A^2)=A\delta(A)+A^*\delta(A)$, 则称$\delta$~是一个可加Jordan左$*$-导子. 在本文中, 我们证明了复的单位$C^*$- 代数到其Banach左模的每个可加Jordan左$*$-导子都恒等于零. 设$G\in\mathcal A$, 如果对任意$A,B\in \mathcal A$, 当$AB=G$时, 有$\delta(AB)=A\delta(B)+B^*\delta(A)$, 则称$\delta$在$G$处左$*$-可导. 我们证明了复的单位$C^*$-代数到其Banach左模的在单位点处左$*$-可导的连续可加映射恒等于零. 相似文献
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Let R be a ring with an endomorphism α and an α-derivation δ. We introduce the notions of symmetric α-rings and weak symmetric α-rings which are generalizations of symmetric rings and weak symmetric rings, respectively, discuss the relations between symmetricα-rings and related rings and investigate their extensions. We prove that if R is a reduced ring and α(1) = 1, then R is a symmetric α-ring if and only if R[x]/(x n) is a symmetric ˉα-ring for any positive integer n. Moreover, it is proven that if R is a right Ore ring, α an automorphism of R and Q(R) the classical right quotient ring of R, then R is a symmetric α-ring if and only if Q(R) is a symmetric ˉα-ring. Among others we also show that if a ring R is weakly 2-primal and(α, δ)-compatible, then R is a weak symmetric α-ring if and only if the Ore extension R[x; α, δ] of R is a weak symmetric ˉα-ring. 相似文献
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It is shown that continuous -local derivations on -algebras are derivations and surjective -local *-automorphisms on prime -algebras or on -algebras such that the identity element is properly infinite are *-automorphisms.
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Lyudmila Turowska 《Proceedings of the American Mathematical Society》2002,130(10):3051-3065
We study the complexity of the problem to describe, up to unitary equivalence, representations of -algebras by unbounded operators on a Hilbert space. A number of examples are developed in detail.
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Assume that N, F and G are groups. If there exsits a normal subgroup of G such that≌ G and G/≌ F, then G is called a central extension of N by F. In this paper, the central extension of N by a minimal non-abelian p-group is determined, where N is an elementary abelian p-group of order p~3. Together with our previous work, all central extensions of N by a minimal non-abelian p-group is determined, where N is an elementary abelian p-group. 相似文献
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In this paper, we obtain generalized Hyers--Ulam stability results of a $(m,n)$-Cauchy-Jensen functional equation associated with approximate Lie $*$-derivations on $\rho$-complete convex modular $*$-algebras $\chi_\rho$ with $\Delta_\mu$-condition on the convex modular $\rho$. 相似文献