منابع مشابه
NONNIL-NOETHERIAN MODULES OVER COMMUTATIVE RINGS
In this paper we introduce a new class of modules which is closely related to the class of Noetherian modules. Let $R$ be a commutative ring with identity and let $M$ be an $R$-module such that $Nil(M)$ is a divided prime submodule of $M$. $M$ is called a Nonnil-Noetherian $R$-module if every nonnil submodule of $M$ is finitely generated. We prove that many of the properties of Noetherian modul...
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We investigate width and Krull–Gabriel dimension over commutative Noetherian rings which are “tame” according to the Klingler–Levy analysis in [4], [5] and [6], in particular over Dedekind-like rings and their homomorphic images. We show that both are undefined in most cases.
متن کاملOn the Grade of Modules over Noetherian Rings
Let be a left and right noetherian ring and mod the category of finitely generated left -modules. In this article, we show the following results. 1 For a positive integer k, the condition that the subcategory of mod consisting of i-torsionfree modules coincides with the subcategory of mod consisting of i-syzygy modules for any 1 ≤ i ≤ k is left-right symmetric. 2 If is an -Gorenstein ring and N...
متن کاملGorenstein syzygy modules
Article history: Received 26 March 2009 Available online 23 October 2010 Communicated by Efim Zelmanov MSC: 16E05 16E10
متن کاملPure-injective Modules over Right Noetherian Serial Rings
We give a criterion for the existence of a super-decomposable pure-injective module over an arbitrary serial ring.
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1996
ISSN: 0021-8693
DOI: 10.1006/jabr.1996.0212