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On \(V\)-modules relative to torsion theory. (English) Zbl 0845.16025

Gardner, B. J. (ed.) et al., Rings and radicals. Proceedings of the international conference, Shijiazhuang, China, 1994. Harlow: Longman. Pitman Res. Notes Math. Ser. 346, 249-252 (1996).
A ring \(R\) is called a left (right) \(V\)-ring if every simple left (right) \(R\)-module is injective. C. Faith called such rings \(V\)-rings after Villamayor who characterized left \(V\)-rings as those in which every left ideal is an intersection of maximal left ideals. The notion of \(V\)-rings has been extended to modules and called “Co-semisimple” by K. R. Fuller. Recently an extensive study of \(V\)-rings and their generalizations has been carried out by various authors. It is well known that a \(V\)-ring is fully idempotent. K. Varadarajan and K. Wehrhahn proved a similar result for \(p\)-\(V\)-rings relative to torsion theories. The present paper generalizes this results for a \(V\)-module relative to torsion theories, we shall prove that every locally projective \(V\)-module is fully right idempotent.
For the entire collection see [Zbl 0839.00021].

MSC:

16S90 Torsion theories; radicals on module categories (associative algebraic aspects)
16D50 Injective modules, self-injective associative rings
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