Topologically semiperfect rings
Enrico Gregorio (1991)
Rendiconti del Seminario Matematico della Università di Padova
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Enrico Gregorio (1991)
Rendiconti del Seminario Matematico della Università di Padova
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Kalathoor Varadarajan (1992)
Publicacions Matemàtiques
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The aim of the present paper is to study Hopfian and Co-Hopfian objects in categories like the category of rings, the module categories A-mod and mod-A for any ring A. Using Stone's representation theorem any Boolean ring can be regarded as the ring A of clopen subsets of compact Hausdorff totally disconnected space X. It turns out that the Boolean ring A will be Hopfian (resp. co-Hopfian) if and only if the space X is co-Hopfian (resp. Hopfian) in the category . For any compact Hausdorff...
D. N. Dikranjan, E. Gregorio, A. Orsatti (1991)
Rendiconti del Seminario Matematico della Università di Padova
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Jan Trlifaj (1982)
Commentationes Mathematicae Universitatis Carolinae
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Daniel Simson (1984)
Rendiconti del Seminario Matematico della Università di Padova
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Claudia Menini (1984)
Rendiconti del Seminario Matematico della Università di Padova
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E. Gregorio (1988)
Rendiconti del Seminario Matematico della Università di Padova
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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.