Generalized -rings and von Neumann regular rings
Giuseppe Baccella (1984)
Rendiconti del Seminario Matematico della Università di Padova
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Giuseppe Baccella (1984)
Rendiconti del Seminario Matematico della Università di Padova
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Koşan, M.Tamer (2006)
International Journal of Mathematics and Mathematical Sciences
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Vedadi, M.R. (2009)
Acta Mathematica Universitatis Comenianae. New Series
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Abdelfattah Haily, Mostafa Alaoui (2001)
Publicacions Matemàtiques
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If M is a simple module over a ring R then, by the Schur's lemma, the endomorphism ring of M is a division ring. However, the converse of this result does not hold in general, even when R is artinian. In this short note, we consider perfect rings for which the converse assertion is true, and we show that these rings are exactly the primary decomposable ones.
Jan Trlifaj (1982)
Commentationes Mathematicae Universitatis Carolinae
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José L. Gómez Pardo (1989)
Extracta Mathematicae
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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...
Carl Faith (1990)
Publicacions Matemàtiques
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In this paper we study a condition right FGTF on a ring R, namely when all finitely generated torsionless right R-modules embed in a free module. We show that for a von Neuman regular (VNR) ring R the condition is equivalent to every matrix ring R is a Baer ring; and this is right-left symmetric. Furthermore, for any Utumi VNR, this can be strengthened: R is FGTF iff R is self-injective.
Kamran Divaani-Aazar, Mohammad Ali Esmkhani, Massoud Tousi (2009)
Colloquium Mathematicae
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Using the notion of cyclically pure injective modules, a characterization of rings which are locally valuation rings is established. As applications, new characterizations of Prüfer domains and pure semisimple rings are provided. Namely, we show that a domain R is Prüfer if and only if two of the three classes of pure injective, cyclically pure injective and RD-injective modules are equal. Also, we prove that a commutative ring R is pure semisimple if and only if every R-module is cyclically...