Displaying similar documents to “On rings whose flat modules form a Grothendieck category”

Finite presentation and purity in categories σ[M]

Mike Prest, Robert Wisbauer (2004)

Colloquium Mathematicae

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For any module M over an associative ring R, let σ[M] denote the smallest Grothendieck subcategory of Mod-R containing M. If σ[M] is locally finitely presented the notions of purity and pure injectivity are defined in σ[M]. In this paper the relationship between these notions and the corresponding notions defined in Mod-R is investigated, and the connection between the resulting Ziegler spectra is discussed. An example is given of an M such that σ[M] does not contain any non-zero finitely...

Morita duality for Grothendieck categories.

José L. Gómez Pardo, Francisco de A. Guil Asensio (1992)

Publicacions Matemàtiques

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We survey some recent results on the theory of Morita duality for Grothendieck categories, comparing two different versions of this concept, and giving applications to QF-3 and Qf-3' rings.

Kasch bimodules

D. N. Dikranjan, E. Gregorio, A. Orsatti (1991)

Rendiconti del Seminario Matematico della Università di Padova

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A duality result for almost split sequences

Lidia Hügel, Helmut Valenta (1999)

Colloquium Mathematicae

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Over an artinian hereditary ring R, we discuss how the existence of almost split sequences starting at the indecomposable non-injective preprojective right R-modules is related to the existence of almost split sequences ending at the indecomposable non-projective preinjective left R-modules. This answers a question raised by Simson in [27] in connection with pure semisimple rings.

Rings whose modules are finitely generated over their endomorphism rings

Nguyen Viet Dung, José Luis García (2009)

Colloquium Mathematicae

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A module M is called finendo (cofinendo) if M is finitely generated (respectively, finitely cogenerated) over its endomorphism ring. It is proved that if R is any hereditary ring, then the following conditions are equivalent: (a) Every right R-module is finendo; (b) Every left R-module is cofinendo; (c) R is left pure semisimple and every finitely generated indecomposable left R-module is cofinendo; (d) R is left pure semisimple and every finitely generated indecomposable left R-module...