T-Rickart modules

S. Ebrahimi Atani; M. Khoramdel; S. Dolati Pish Hesari

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Displaying similar documents to “T-Rickart modules”

On FI-mono-retractable modules

Marziyeh Atashkar, Yahya Talebi (2022)

Commentationes Mathematicae Universitatis Carolinae

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We introduce the notion of FI-mono-retractable modules which is a generalization of compressible modules. We investigate the properties of such modules. It is shown that the rings over which every cyclic module is FI-mono-retractable are simple Noetherian $V$ -ring with zero socle or Artinian semisimple. The last section of the paper is devoted to the endomorphism rings of FI-retractable modules.

Commutative rings whose certain modules decompose into direct sums of cyclic submodules

Farid Kourki, Rachid Tribak (2023)

Czechoslovak Mathematical Journal

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We provide some characterizations of rings $R$ for which every (finitely generated) module belonging to a class $𝒞$ of $R$ -modules is a direct sum of cyclic submodules. We focus on the cases, where the class $𝒞$ is one of the following classes of modules: semiartinian modules, semi-V-modules, V-modules, coperfect modules and locally supplemented modules.

Limits of tilting modules

Clezio A. Braga, Flávio U. Coelho (2009)

Colloquium Mathematicae

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We study the problem of when a direct limit of tilting modules is still a tilting module.

Strongly rectifiable and S-homogeneous modules

Libuše Tesková (2000)

Discussiones Mathematicae - General Algebra and Applications

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In this paper we introduce the class of strongly rectifiable and S-homogeneous modules. We study basic properties of these modules, of their pure and refined submodules, of Hill's modules and we also prove an extension of the second Prüfer's theorem.

Estimates of global dimension

Wei Jiaqun (2006)

Czechoslovak Mathematical Journal

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In this note we show that for a $*^{n}$ -module, in particular, an almost $n$ -tilting module, $P$ over a ring $R$ with $A = {E n d}_{R} P$ such that $P_{A}$ has finite flat dimension, the upper bound of the global dimension of $A$ can be estimated by the global dimension of $R$ and hence generalize the corresponding results in tilting theory and the ones in the theory of $*$ -modules. As an application, we show that for a finitely generated projective module over a VN regular ring $R$ , the global dimension of its endomorphism ring...

Retraction notice to: “α-modules and generalized submodules”

Pasha Zusmanovich (2019)

Communications in Mathematics

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Complete differentials of higher order in linear field modules

Jan Kubarski (1984)

Annales Polonici Mathematici

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Rigidity of generalized Verma modules

Oleksandr Khomenko, Volodymyr Mazorchuk (2002)

Colloquium Mathematicae

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We prove that generalized Verma modules induced from generic Gelfand-Zetlin modules, and generalized Verma modules associated with Enright-complete modules, are rigid. Their Loewy lengths and quotients of the unique Loewy filtrations are calculated for the regular block of the corresponding category 𝒪(𝔭,Λ).

Strongly $𝒲$ -Gorenstein modules

Husheng Qiao, Zongyang Xie (2013)

Czechoslovak Mathematical Journal

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Let $𝒲$ be a self-orthogonal class of left $R$ -modules. We introduce a class of modules, which is called strongly $𝒲$ -Gorenstein modules, and give some equivalent characterizations of them. Many important classes of modules are included in these modules. It is proved that the class of strongly $𝒲$ -Gorenstein modules is closed under finite direct sums. We also give some sufficient conditions under which the property of strongly $𝒲$ -Gorenstein module can be inherited by its submodules and quotient...

Some remarks on Prüfer modules

S. Ebrahimi Atani, S. Dolati Pishhesari, M. Khoramdel (2013)

Discussiones Mathematicae - General Algebra and Applications

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We provide several characterizations and investigate properties of Prüfer modules. In fact, we study the connections of such modules with their endomorphism rings. We also prove that for any Prüfer module M, the forcing linearity number of M, fln(M), belongs to {0,1}.

Gorenstein star modules and Gorenstein tilting modules

Peiyu Zhang (2021)

Czechoslovak Mathematical Journal

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We introduce the notion of Gorenstein star modules and obtain some properties and a characterization of them. We mainly give the relationship between $n$ -Gorenstein star modules and $n$ -Gorenstein tilting modules, see L. Yan, W. Li, B. Ouyang (2016), and a new characterization of $n$ -Gorenstein tilting modules.