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.
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.
Gabriella D'Este, Dieter Happel (1990)
Rendiconti del Seminario Matematico della Università di Padova
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Husheng Qiao, Zongyang Xie (2013)
Czechoslovak Mathematical Journal
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Let be a self-orthogonal class of left -modules. We introduce a class of modules, which is called strongly -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 -Gorenstein modules is closed under finite direct sums. We also give some sufficient conditions under which the property of strongly -Gorenstein module can be inherited by its submodules and quotient...
Timothy Porter (1983)
Cahiers de Topologie et Géométrie Différentielle Catégoriques
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T. Nakayama (1964)
Acta Arithmetica
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Edgar E. Enochs, Overtoun M. G. Jenda, Luis Oyonarte (2001)
Rendiconti del Seminario Matematico della Università di Padova
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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.