共查询到20条相似文献,搜索用时 173 毫秒
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(1)设R是左连续环,则R是左Artin环当且仅当R满足左限制有限条件当且仅当R关于本质左理想满足极小条件当且仅当R关于本质左理想满足极大条件.同时给出一个左自内射环是QF环的充要条件;(2)证明了左Z1-环上的有限生成模都有Artin-Rees性质. 相似文献
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On perfect simple-injective rings 总被引:4,自引:0,他引:4
Harada calls a ring right simple-injective if every -homomorphism with simple image from a right ideal of to is given by left multiplication by an element of . In this paper we show that every left perfect, left and right simple-injective ring is quasi-Frobenius, extending a well known result of Osofsky on self-injective rings. It is also shown that if is left perfect and right simple-injective, then is quasi-Frobenius if and only if the second socle of is countably generated as a left -module, extending many recent results on self-injective rings. Examples are given to show that our results are non-trivial extensions of those on self-injective rings.
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V. I. Gemintern 《Mathematical Notes》1969,6(5):776-780
It is shown that the ring of endomorphisms of an arbitrary free R-module is right self-injective if and only if R is quasi-Frobenius.Translated from Matematicheskie Zametki, Vol. 6, No. 5, pp. 533–540, November, 1969.We take this opportunity to thank L. A. Skornyakov for his guidance. 相似文献
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Inge Schellong 《manuscripta mathematica》1975,15(1):81-89
Let F denote a field of characteristic ≠2. The Witt ring WF (i.e. the ring of similarity classes of quadratic forms with coefficients in F) will be characterized by taking the similarity classes of certain Pfister forms [2] as generators and using suitable relations among them (theorem 1). In order to characterize GF, the graded ring associated to WF, in terms of generators and relations Milnor [4] constructed a homomorphism from his ring k*F onto GF and conjectured this homomorphism to be an isomorphism. This conjecture turns out to be equivalent to a problem on ideals in a commutative ring (theorem 2). 相似文献
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In this article we present some results about bounded factorization rings (BFRs), i.e., commutative rings with the property that each nonzero nonunit has a bound on the length of its factorizations into nonunits. In their article Factorization in Commutative Rings with Zero Divisors, Anderson and Valdes-Leon conjectured that R[x], the polynomial ring over R, is a bounded factorization ring if and only if R is a BFR and 0 is primary in R. We give some conditions under which the conjecture is true and present a bounded factorization ring with 0 primary where the polynomial ring is not a BFR. 相似文献
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F. Couchot 《Journal of Pure and Applied Algebra》2007,211(1):235-247
Let R be a valuation ring and let Q be its total quotient ring. It is proved that any singly projective (respectively flat) module is finitely projective if and only if Q is maximal (respectively artinian). It is shown that each singly projective module is a content module if and only if any non-unit of R is a zero-divisor and that each singly projective module is locally projective if and only if R is self-injective. Moreover, R is maximal if and only if each singly projective module is separable, if and only if any flat content module is locally projective. Necessary and sufficient conditions are given for a valuation ring with non-zero zero-divisors to be strongly coherent or π-coherent.A complete characterization of semihereditary commutative rings which are π-coherent is given. When R is a commutative ring with a self-FP-injective quotient ring Q, it is proved that each flat R-module is finitely projective if and only if Q is perfect. 相似文献
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Dimitrios Ballas 《代数通讯》2017,45(2):481-492
In this paper, we show that the injective dimension of all projective modules over a countable ring is bounded by the self-injective dimension of the ring. We also examine the extent to which the flat length of all injective modules is bounded by the flat length of an injective cogenerator. To that end, we study the relation between these finiteness conditions on the ring and certain properties of the (strict) Mittag–Le?er modules. We also examine the relation between the self-injective dimension of the integral group ring of a group and Ikenaga’s generalized (co-)homological dimension. 相似文献
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Alex S. Dugas 《Journal of Pure and Applied Algebra》2010,214(6):990-170
We say that an algebra A is periodic if it has a periodic projective resolution as an (A,A)-bimodule. We show that any self-injective algebra of finite representation type is periodic. To prove this, we first apply the theory of smash products to show that for a finite Galois covering B→A, B is periodic if and only if A is. In addition, when A has finite representation type, we build upon results of Buchweitz to show that periodicity passes between A and its stable Auslander algebra. Finally, we use Asashiba’s classification of the derived equivalence classes of self-injective algebras of finite type to compute bounds for the periods of these algebras, and give an application to stable Calabi-Yau dimensions. 相似文献
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D. V. Tyukavkin 《Algebra and Logic》1994,33(5):315-321
Regular, right self-injective rings are considered. We settle the question of when such a ring is a right V-ring, i.e., when each simple right module over the ring is injective. It is proved that a regular, right self-injective V-ring of the power of the continuum has a bounded nilpotency index.Translated fromAlgebra i Logika, Vol. 33, No. 5, pp. 564–575, September–October, 1994. 相似文献
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Ehsan Momtahan 《代数通讯》2013,41(11):4167-4171
A well-known result by Y. Utumi states: Every right or left self-injective ring is von Neumann regular modulo its Jacobson radical. In this note, we give an example of a commutative ?0-self-injective ring which is not von Neumann regular modulo its Jacobson radical. 相似文献
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On Decompositions of Quasi-Regular Rings 总被引:1,自引:0,他引:1
Hu Xianhui 《东北数学》1994,(2)
OnDecompositionsofQuasi-RegularRings¥HuXianhui(胡先惠)(DepartmntofMathematics,theCentralInstituteofNationalities,Beijing,100081)... 相似文献
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We investigate when an exact functor --Γ which induces a stable equivalence is part of a stable equivalence of Morita type. If Λ and Γ are finite dimensional algebras over a field k whose semisimple quotients are separable, we give a necessary and sufficient condition for this to be the case. This generalizes a result of Rickard’s for self-injective algebras. As a corollary, we see that the two functors given by tensoring with the bimodules in a stable equivalence of Morita type are right and left adjoints of one another, provided that these bimodules are indecomposable. This fact has many interesting consequences for stable equivalences of Morita type. In particular, we show that a stable equivalence of Morita type induces another stable equivalence of Morita type between certain self-injective algebras associated to the original algebras. We further show that when there exists a stable equivalence of Morita type between Λ and Γ, it is possible to replace Λ by a Morita equivalent k-algebra Δ such that Γ is a subring of Δ and the induction and restriction functors induce inverse stable equivalences. 相似文献
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《代数通讯》2013,41(9):4175-4178
Abstract A ring Ris Dedekind Finite(=DF) if xy = 1 implies yx = 1 for all x, yin R. Obviously any subring of a DFring Ris DF. The object of the paper is to generalize, and give a radically new proof of a theorem of Kaplansky on group algebras that are Dedekind finite. We shall prove that all right subrings of right and left self-injective (in fact, continuous) rings are DF. 相似文献
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David L. Webb 《K-Theory》1987,1(4):417-422
The formula for the G-theory of the group ring of a finite group G conjectured by Hambleton, Taylor, and Williams is shown to be valid for ¦G¦ square-free. 相似文献
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A. Mohammadian 《代数通讯》2013,41(3):988-994
The commuting graph of a ring R, denoted by Γ(R), is a graph whose vertices are all noncentral elements of R and two distinct vertices are joint by an edge whenever they commute. It is conjectured that if R is a ring with identity such that Γ(R) ≈ Γ(M n (F)), for a finite field F and n ≥ 2, then R ≈ M n (F). Here we prove this conjecture when n = 2. 相似文献