On some properties of pure morphisms of commutative rings.
Mesablishvili, Bachuki (2002)
Theory and Applications of Categories [electronic only]
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Mesablishvili, Bachuki (2002)
Theory and Applications of Categories [electronic only]
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Markus Schmidmeier (1998)
Colloquium Mathematicae
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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...
Daniel Simson (1977)
Fundamenta Mathematicae
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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.
D. N. Dikranjan, E. Gregorio, A. Orsatti (1991)
Rendiconti del Seminario Matematico della Università di Padova
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Li, Linlin, Wei, Jiaqun (2008)
Matematichki Vesnik
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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.
J. L. García Hernández, J. L. Gómez Pardo (1987)
Extracta Mathematicae
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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...
Daniel Simson, Andrzej Skowroński (1978)
Fundamenta Mathematicae
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