Retraction notice to: “α-modules and generalized submodules”
Pasha Zusmanovich (2019)
Communications in Mathematics
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Pasha Zusmanovich (2019)
Communications in Mathematics
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Roman Sikorski (1971)
Colloquium Mathematicae
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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).
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.
D. D. Anderson (1977)
Colloquium Mathematicae
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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}.
Jan Kubarski (1984)
Annales Polonici Mathematici
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Otto Kerner, Frank Lukas (1996)
Mathematische Zeitschrift
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Naoum, Adil G., Al-Shalgy, Layla S.M. (2000)
Beiträge zur Algebra und Geometrie
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Clezio Braga, Flávio Coelho (2008)
Open Mathematics
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We discuss the existence of tilting modules which are direct limits of finitely generated tilting modules over tilted algebras.
Andrzej Skowroński (1984)
Colloquium Mathematicae
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Mike Prest, Gena Puninski (2004)
Colloquium Mathematicae
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We classify one-directed indecomposable pure injective modules over finite-dimensional string algebras.
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.
John Dauns (1991)
Forum mathematicum
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Dieter Happel, Luise Unger (1990)
Banach Center Publications
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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.
Claus Ringel (1998)
Colloquium Mathematicae
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Karin Erdmann, José Antonio de la Peña, Corina Sáenz (2002)
Colloquium Mathematicae
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Let A be a finite-dimensional algebra which is quasi-hereditary with respect to the poset (Λ, ≤), with standard modules Δ(λ) for λ ∈ Λ. Let ℱ(Δ) be the category of A-modules which have filtrations where the quotients are standard modules. We determine some inductive results on the relative Auslander-Reiten quiver of ℱ(Δ).