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1.
设环A是环B的扩环(记作A/B),B是QF环,在本文中我们将证明在以下四种情形下A也是QF环:(1)BA是有限生成自由的且A/B是投射扩张.(2)A/B是Frobenius的.(3)A/B是可离且平坦的.(4)A/B是H-可离的. 相似文献
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二次系统的二重极限环和以无限大分界线环分支出两个极限环的例子 总被引:6,自引:1,他引:5
二次系统的二重极限环和以无限大分界线环分支出两个极限环的例子沈伯骞,何平(辽宁师范大学数学系,大连116022)(辽宁警官专科学校,大连116033)EXAMPLESOFONEDOUBLELIMITCYCLEORTWOSINGLELIMITCYCLE... 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R#G是正则的当且仅当MG(R)是gr-正则的当且仅当对每个λ∈G和G的任意非空子集H和F,MH×F(R)的每个矩阵都有1-逆。(2)当G是任意群,G-型分次环R是反gr-正则的当且仅当F(R#G)是反正则的当且仅当对每个λ∈G和G的任意非空子集H和K,FMH×F(R)的每个矩阵有2-逆当且仅当FMG(R)是gr-反正则的。 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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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
9.
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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本文主要讨论欧氏整环上线性群一类子群的结构,并获得其一类极大子群, 相似文献
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Huanyin Chen 《Southeast Asian Bulletin of Mathematics》2001,25(1):15-21
In this paper, we investigate generalized s-comparability over regular rings. These also give generalizations of the corresponding results over regular rings satisfying general comparability.AMS Subject Classification (1991) 16A30 16E50 相似文献
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Hans-Gert Gräbe 《Results in Mathematics》1989,15(3-4):202-220
The aim of this paper is to prove that many homological properties and estimates of the discrete straightening ring still remain valid for the straightening ring itself. E.g. Cohen-Macaulay property, generalised Cohen-Macaulay property and Serre condition (Sn) (the latter for unmixed discrete straightening rings) transfer. The main technical tool is a further development of a spectral sequence argument well known in the case of associated graded rings. 相似文献
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The relationship between the Ziegler spectrum of (the category of modules over) a ring and the Ziegler spectrum of its derived
category is investigated. Over von Neumann regular rings and hereditary rings the spectrum of the derived category is a disjoint
union of copies of the spectrum of the ring but in general there are further indecomposable pure-injective objects of the
derived category.
Presented by A. Verschoren
Mathematics Subject Classifications (2000) Primary: 18E30; secondary: 03C60. 相似文献
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Bernhard Banaschewski 《Mathematical Logic Quarterly》1994,40(4):478-480
In the present note we give a direct deduction of the Axiom of Choice from the Maximal Ideal Theorem for commutative rings with unit. Mathematics Subject Classification: 03E25, 04A25, 13A15. 相似文献
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Huanyin Chen 《Southeast Asian Bulletin of Mathematics》2000,24(1):19-24
In this paper, we investigate diagonal reductions of matrices over generalized stable exchange rings. We show that every regular matirx over generalized stable exchange rings with stable range 2 admits power diagonal reduction.AMS Subject Classification (1991): 16A30 16E50This work was supported by the National Natural Science Foundation of China. 相似文献
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Danielle Salles 《代数通讯》2013,41(11):3511-3525
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Faith Carl 《代数通讯》2013,41(6):559-571
For a ring R, the following two conditions are equivalent:. (1) If E is an indecomposable injective right R-module, then End ER is a field (not necesarily commutative). (2) Every co-irreducible rigtht ideal is critical. Since (2) has been characterized ideal-theoretically, this amounts to an ideal-theoretical characterization of (1). These rings come up to the study of (QI) rings in which every quasi-injective module is injective. 相似文献
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The famous BurnsideSchur theorem states that every primitivefinite permutation group containing a regular cyclic subgroupis either 2-transitive or isomorphic to a subgroup of a 1-dimensionalaffine group of prime degree. It is known that this theoremcan be expressed as a statement on Schur rings over a finitecyclic group. Generalizing the latter, Schur rings are introducedover a finite commutative ring, and an analogue of this statementis proved for them. Also, the finite local commutative ringsare characterized in permutation group terms. 2000 MathematicsSubject Classification 20B10, 20B15, 05E99. 相似文献