T-Rickart modules

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

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Displaying similar documents to “T-Rickart 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...

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}.

$\oplus$ -cofinitely supplemented modules

H. Çalışıcı, A. Pancar (2004)

Czechoslovak Mathematical Journal

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Let $R$ be a ring and $M$ a right $R$ -module. $M$ is called $\oplus$ -cofinitely supplemented if every submodule $N$ of $M$ with $\frac{M}{N}$ finitely generated has a supplement that is a direct summand of $M$ . In this paper various properties of the $\oplus$ -cofinitely supplemented modules are given. It is shown that (1) Arbitrary direct sum of $\oplus$ -cofinitely supplemented modules is $\oplus$ -cofinitely supplemented. (2) A ring $R$ is semiperfect if and only if every free $R$ -module is $\oplus$ -cofinitely supplemented. In addition, if $M$ has the...

Wakamatsu tilting modules with finite injective dimension

Guoqiang Zhao, Lirong Yin (2013)

Czechoslovak Mathematical Journal

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Let $R$ be a left Noetherian ring, $S$ a right Noetherian ring and $_{R} ω$ a Wakamatsu tilting module with $S = End (_{R} ω)$ . We introduce the notion of the $ω$ -torsionfree dimension of finitely generated $R$ -modules and give some criteria for computing it. For any $n \geq 0$ , we prove that ${l . id}_{R} (ω) = {r . id}_{S} (ω) \leq n$ if and only if every finitely generated left $R$ -module and every finitely generated right $S$ -module have $ω$ -torsionfree dimension at most $n$ , if and only if every finitely generated left $R$ -module (or right $S$ -module) has generalized Gorenstein...

Differential modules

Roman Sikorski (1971)

Colloquium Mathematicae

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The Ziegler spectrum of a tame hereditary algebra

Claus Ringel (1998)

Colloquium Mathematicae

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Modules for which the natural map of the maximal spectrum is surjective

H. Ansari-Toroghy, R. Ovlyaee-Sarmazdeh (2010)

Colloquium Mathematicae

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Let R be a commutative ring with identity. The purpose of this paper is to introduce two new classes of modules over R, called Ms modules and fulmaximal modules respectively. The first (resp. second) class contains the family of finitely generated and primeful (resp. finitely generated and multiplication) modules properly. Our concern is to extend some properties of primeful and multiplication modules to these new classes of modules.