Displaying similar documents to “When does an AB5* module have finite hollow dimension?”

Fleury's spanning dimension and chain conditions on non-essential elements in modular lattices

Christian Lomp, A. Çiğdem Özcan (2011)

Colloquium Mathematicae

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Based on a lattice-theoretic approach, we give a complete characterization of modules with Fleury's spanning dimension. An example of a non-Artinian, non-hollow module satisfying this finiteness condition is constructed. Furthermore we introduce and characterize the dual notion of Fleury's spanning dimension.

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.

The existence of relative pure injective envelopes

Fatemeh Zareh-Khoshchehreh, Kamran Divaani-Aazar (2013)

Colloquium Mathematicae

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Let 𝓢 be a class of finitely presented R-modules such that R∈ 𝓢 and 𝓢 has a subset 𝓢* with the property that for any U∈ 𝓢 there is a U*∈ 𝓢* with U* ≅ U. We show that the class of 𝓢-pure injective R-modules is preenveloping. As an application, we deduce that the left global 𝓢-pure projective dimension of R is equal to its left global 𝓢-pure injective dimension. As our main result, we prove that, in fact, the class of 𝓢-pure injective R-modules is enveloping.

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).

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}.

Weak Krull-Schmidt theorem

Ladislav Bican (1998)

Commentationes Mathematicae Universitatis Carolinae

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Recently, A. Facchini [3] showed that the classical Krull-Schmidt theorem fails for serial modules of finite Goldie dimension and he proved a weak version of this theorem within this class. In this remark we shall build this theory axiomatically and then we apply the results obtained to a class of some modules that are torsionfree with respect to a given hereditary torsion theory. As a special case we obtain that the weak Krull-Schmidt theorem holds for the class of modules that are...

On large selforthogonal modules

Gabriella D'Este (2006)

Commentationes Mathematicae Universitatis Carolinae

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We construct non faithful direct summands of tilting (resp. cotilting) modules large enough to inherit a functorial tilting (resp. cotilting) behaviour.