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设M是任意环类,u,ψ分别表示上根算子及半单算子。W.G.Leavitt在[1]中研究了uM成为遗传根的充要条件。本文将讨论ψM成为半单类,本质闭类,同态闭类或具有其它环类性质的一些等价条件。作为推论,最后给 相似文献
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代数正规类中的遗传根与强半单根 总被引:5,自引:0,他引:5
Puczylowski建立了一般代数对象类的根理论.本文在代数正规类中,用格论方法刻划一般遗传根和强半单根类,探究它们的一些性质,推广了已知各类代数系统的某些根论研究. 相似文献
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σ-根与σ-半单类的构造 总被引:1,自引:0,他引:1
继[1~3]分别给出σ-根及其半单类的两个特征性质,研究了对于已知环类M,含于M的最大σ-根及σ-半单类和包含M的最小σ-半单类的构造,同时得到σ-半单闭包σ-遗传的一个充分条件. 相似文献
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本文讨论在什么条件下(α∶β)是根环类的问题,在假定α为优(Superior)根的条件下分别得出(α∶β)为根类,为遗传根类的充要条件,作为应用具体地给出双正则根,强正则根的补根. 相似文献
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A. A. Tuganbaev 《Journal of Mathematical Sciences》2005,128(6):3496-3500
Let A be a right and left distributive ring. For a positive integer n, we obtain a criterion of projectivity of all n-generated right ideals of the ring A and a criterion of the right semi-heredity of the ring A.__________Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 9, No. 1, pp. 253–258, 2003. 相似文献
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Let A be an order integral over a valuation ring V in a centralsimple F-algebra, where F is the fraction field of V. We showthat (a) if (Vh, Fh) is the Henselization of (V, F), then Ais a semihereditary maximal order if and only if AVVh is a semihereditarymaximal order, generalizing the result by Haile, Morandi andWadsworth, and (b) if J(V) is a principal ideal of V, then asemihereditary V-order is an intersection of finitely many conjugatesemihereditary maximal orders; if not, then there is only onemaximal order containing the V-order. 1991 Mathematics SubjectClassification 16H05. 相似文献
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François Couchot 《代数通讯》2013,41(9):2685-2692
We prove that each almost local-global semihereditary ring R has the stacked bases property and is almost Bézout. More precisely, if M is a finitely presented module, its torsion part tM is a direct sum of cyclic modules where the family of annihilators is an ascending chain of invertible ideals. These ideals are invariants of M. Moreover, M/tM is a projective module which is isomorphic to a direct sum of finitely generated ideals. These ideals allow us to define a finitely generated ideal whose isomorphism class is an invariant of M. The idempotents and the positive integers defined by the rank of M/tM are invariants of M too. It follows that each semihereditary ring of Krull-dimension one or of finite character, in particular each hereditary ring, has the stacked base property. These results were already proved for Prüfer domains by Brewer, Katz, Klinger, Levy, and Ullery. It is also shown that every semihereditary Bézout ring of countable character is an elementary divisor ring. 相似文献
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In this paper the sufficient and necessary conditions are given for a formal triangular matrix ring to be right PP, generalized right PP, or semihereditary, respectively. 相似文献
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Yang Zhang 《代数通讯》2013,41(1):373-381
Some necessary and sufficient conditions are given for rings of the Morita contexts to be semihereditary maximal V-orders, Prüfer rings and Dubrovin valuation rings. 相似文献
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No Abstract. June 30, 1998 相似文献
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Richard Wiegandt 《东北数学》1995,(4)
ANoteonSupplementingRadicalsRichardWiegandt(MathematicalInstitute,HungarianAcademyofSciences,P.O.Box127,Budapest,Hungary)Abst... 相似文献