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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A new duality theorem for semisimple modules and characterization of Villamayor rings


Authors: Carl Faith and Pere Menal
Journal: Proc. Amer. Math. Soc. 123 (1995), 1635-1637
MSC: Primary 16E50
MathSciNet review: 1254836
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Abstract: We prove the theorem: If R is a ring whose right ideals satisfy the double annihilator condition with respect to a semisimple right R-module W, then every right ideal is an intersection of maximal right ideals, consequently R is a right V (for Villamayor) ring, and W is then necessarily a cogenerator of $ \bmod$-$ R$. (The converse is well known.) We use this to give a new proof of a theorem of ours on right Johns rings.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1995-1254836-6
PII: S 0002-9939(1995)1254836-6
Article copyright: © Copyright 1995 American Mathematical Society