共查询到20条相似文献,搜索用时 62 毫秒
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在此文中,我们对Strong-Armendariz环和Baer PP及PS环Ore-扩张R[x,x~(-1);α]的一些性质进行了讨论研究,并得到了一些结果.主要证明了R是Baer(PP)环当且仅当R[[x]]是Baer(PP)环及R是α-rigid环时,R是Baer(PP,PS)环当且仅当R[[x]]是Baer(PP,PS)环. 相似文献
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通过引用P-平坦模的定义,引入了右IPF环的概念,推广了右IF环的概念,这对研究IF环及QF环具有重要的作用,同时对右IPF环的性质作了一些刻画,得到了右IPF环的若干个等价命题;最后,用P-平坦模及右IPF环推出了正则环的一些等价条件. 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
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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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研究了每一个极大左理想是弱右理想的环的性质.得到了左SF-环和强正则环的一些新的刻画,推广了一些已知的结论. 相似文献
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极小条件环中的左理想的因子分解王元金(辽宁师范大学数学系,大连116022)关键词交换环,素理想,左理想.分类号AMS(1991)13A15/CCLO153.3文献[1]讨论了极小条件环中左理想分解为左素理想之交的问题.本文利用文献[1]的一些结果,... 相似文献
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设R是一个环,其上的理想包含图,记为Γ_I(R),是一个有向图,它以R的非平凡左理想为顶点,从R的左理想I_1到I_2有一条有向边当且仅当I_1真包含于I_2.环R上的理想关系图,记为Γ_i(R),也是一个有向图,它以R为顶点集,从R中元素A到B有一条有向边当且仅当A生成的左理想真包含于B生成的左理想.设F_q为有限域,其上n阶全矩阵环记为M_n(F_q),本文刻画了环M_n(F_q)上的理想包含图以及理想关系图的任意自同构. 相似文献
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Yueming Xiang 《数学研究通讯:英文版》2013,29(2):121-130
A left ideal $I$ of a ring $R$ is small in case for every proper left ideal $K$ of $R,
K +I≠R$. A ring $R$ is called left $PS$-coherent if every principally small left ideal $Ra$ is finitely presented. We develop, in this paper, $PS$-coherent rings as a generalization
of $P$-coherent rings and $J$-coherent rings. To characterize $PS$-coherent rings, we first
introduce $PS$-injective and $PS$-flat modules, and discuss the relation between them
over some spacial rings. Some properties of left $PS$-coherent rings are also studied. 相似文献
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Bruno J. Müller 《代数通讯》2013,41(4):415-441
We give an new proof for the main theorem of [8], ie. that a right-noetherian right-a-homogeneous right-weakly ideal invariant ring has a right-artinian classical right-quotient ring, relating it to the a-tors-ion theory; and we show that for weakly ideal invariant rings satisfying | R/P |l = | R/P |r for all prime ideals P , the clans are Krull homogeneous and can be characterized by various kinds of links. 相似文献
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本文研究了广义幂级数环与其系数环在本质理想和非奇异性上的关系.利用本质理想的定义和性质,得到了广义幂级数环的左理想为本质左理想的菪干充分必要条件.在此基础上,给出了广义幂级数环为左非奇异环的充分必要条件. 相似文献
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Manuel L. Reyes 《代数通讯》2013,41(11):4585-4608
Many classical ring-theoretic results state that an ideal that is maximal with respect to satisfying a special property must be prime. We present a “Prime Ideal Principle” that gives a uniform method of proving such facts, generalizing the Prime Ideal Principle for commutative rings due to T. Y. Lam and the author. Old and new “maximal implies prime” results are presented, with results touching on annihilator ideals, polynomial identity rings, the Artin–Rees property, Dedekind-finite rings, principal ideals generated by normal elements, strongly noetherian algebras, and just infinite algebras. 相似文献
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Let R be a ring with unity. The inclusion ideal graph of a ring R, denoted by In(R), is a graph whose vertices are all nontrivial left ideals of R and two distinct left ideals I and J are adjacent if and only if I ? J or J ? I. In this paper, we show that In(R) is not connected if and only if R ? M 2(D) or D 1 × D 2, for some division rings, D, D 1 and D 2. Moreover, we prove that if In(R) is connected, then diam(In(R)) ≤3. It is shown that if In(R) is a tree, then In(R) is a caterpillar with diam(In(R)) ≤3. Also, we prove that the girth of In(R) belongs to the set {3, 6, ∞}. Finally, we determine the clique number and the chromatic number of the inclusion ideal graph for some classes of rings. 相似文献