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51.
Chin-Pi Lu 《代数通讯》2013,41(3):807-828
Let M be a module over a commutative ring R. A submodule P of M is called prime if P ≠ M and, whenever r ∈ R, e ∈ M, and re ∈ P, we have rM ? P or e ∈ P. We let Spec(M) denote the set of all prime submodules of M. Using a topology analogous to the Zariski topology for Spec(R), we establish necessary and sufficient conditions for Spec(M) to be a Noetherian space. We produce some examples of modules with Noetherian spectrum that have not appeared in the literature previously. In particular, Laskerian modules and faithfully flat modules over Laskerian rings have Noetherian spectra. (The term Laskerian is defined in Section 3.) 相似文献
52.
We establish conditions for Spec(M) to be Noetherian and spectral space, w.r.t. different topologies. We used rings with Noetherian spectrum to produce plentiful examples of modules with Noetherian spectrum that have not appeared in the literature previously. In particular, we show that every ?-module has Noetherian spectrum. Another main subject of this article is presenting the conditions under which a module is top. In particular, we show that every distributive module is top, every content weak multiplication R-module M is also top, and moreover, if R has Noetherian spectrum, then Spec(M) is a spectral space. 相似文献
53.
54.
Mi Hee Park 《代数通讯》2013,41(12):3965-3978
Let Γ be a torsion-free cancellative commutative monoid and let R = ?α∈ΓRα be a commutative Γ-graded ring. We show that if R is a graded Noetherian domain, then its integral closure is a graded Krull domain. This is a graded analog of the Mori–Nagata theorem. We also show that for a graded Strong Mori domain, its complete integral closure is a graded Krull domain but its integral closure is not necessarily a graded Krull domain. 相似文献
55.
本文利用［１］中建立的关系,给出了半素右Ｎｏｅｔｈｃｒ环上所有加性秩函数对应的Ｇａｂｒｉｅｌ拓朴与相应商环的构造,并建立了一般Ｎｏｅｔｈｅｒ环上加性秩函数与Ａｒｔｉｎ环上模范畴中的有限长之间的联系． 相似文献
56.
Susan Elle 《代数通讯》2017,45(3):1323-1346
To study AS-regular algebras of dimension 5, we consider dimension 5 graded iterated Ore extensions generated in degree one. We classify the possible degrees of relations and structure of the free resolution for extensions with 3 and 4 generators. We show that every known type of algebra of dimension 5 can be realized by an Ore extension and we consider which of these types cannot be realized by an enveloping algebra. 相似文献
57.
Richard Resco 《代数通讯》2013,41(10):3013-3017
In this article we construct an affine prime PI ring with a cyclic module whose endomorphism ring is not Jacobson. Then, using similar techniques, we construct an affine prime Noetherian PI ring with a cyclic module whose endomorphism ring is not Noetherian. 相似文献
58.
In this paper we consider serial rings with T-nilpotent prime radical, factor-rings of which by the prime radical are right Noetherian rings. We prove that the prime quiver
of such a ring is a disconnected union of cycles and chains. In the case when the prime quiver of such a serial ring is a
chain the prime radical is nilpotent. For serial rings with nilpotent prime radical we introduce an analogue of Kupisch series.
Presented by Yu. Drozd
Mathematics Subject Classifications (2000) 16P40, 16G10. 相似文献
59.
The notion of semilocal ring is extended to the classes of right G-semilocal and right N-semilocal rings. We explore the algebraic properties of such classes and study their relations with many other rings such as clean, exchange and I-finite rings. Localization of right G-semilocal rings is considered. 相似文献
60.
Yu. É. Trubitsyn 《Mathematical Notes》1997,61(1):96-99
This paper is devoted to the study of semigroups presented by a single defining relationA=B and satisfying the Church-Rosser property.
Translated fromMatematicheskie Zametki, Vol. 61, No. 1, pp. 114–118, January, 1997.
Translated by A. I. Shtern 相似文献