Utumi endomorphism rings of dual modules
José L. Gómez Pardo (1989)
Extracta Mathematicae
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José L. Gómez Pardo (1989)
Extracta Mathematicae
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Tomáš Kepka (1995)
Commentationes Mathematicae Universitatis Carolinae
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The duals of -compact modules are briefly discussed.
Jan Žemlička (2004)
Commentationes Mathematicae Universitatis Carolinae
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The purpose of this paper is to provide a criterion of an occurrence of uncountably generated uniserial modules over chain rings. As we show it suffices to investigate two extreme cases, nearly simple chain rings, i.e. chain rings containing only three two-sided ideals, and chain rings with “many” two-sided ideals. We prove that there exists an -generated uniserial module over every non-artinian nearly simple chain ring and over chain rings containing an uncountable strictly increasing...
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...
Leonid A. Kurdachenko, Igor Ya. Subbotin, Vasyl A. Chupordia (2015)
Commentationes Mathematicae Universitatis Carolinae
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A modular analogue of the well-known group theoretical result about finiteness of the derived subgroup in a group with a finite factor by its center has been obtained.
Patrick. F. Smith, Dinh Van Huynh (1990)
Banach Center Publications
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Kunio Yamagata (2008)
Colloquium Mathematicae
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We characterize the semiregularity of the endomorphism ring of a module with respect to the ideal of endomorphisms with large kernel, and show some new classes of modules with semiregular endomorphism rings.
Robert El Bashir, Tomáš Kepka, Jan Žemlička (2011)
Acta Universitatis Carolinae. Mathematica et Physica
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José Gómez Torrecillas, Blas Torrecillas Jover (1991)
Extracta Mathematicae
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Let R be an associative (not necessarily commutative) ring with unit. The study of flat left R-modules permits to achieve homological characterizations for some kinds of rings (regular Von Neumann, hereditary). Colby investigated in [1] the rings with the property that every left R-module is embedded in a flat left R-module and called them left IF rings. These rings include regular and quasi-Frobenius rings. Another useful tool for the study of non-commutative rings is the classical...