A new duality theorem for semisimple modules and characterization of Villamayor rings
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- by Carl Faith and Pere Menal PDF
- Proc. Amer. Math. Soc. 123 (1995), 1635-1637 Request permission
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 $\bmod \text {-}R$. (The converse is well known.) We use this to give a new proof of a theorem of ours on right Johns rings.References
- Carl Faith, Algebra. I. Rings, modules, and categories, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 190, Springer-Verlag, Berlin-New York, 1981. Corrected reprint. MR 623254 —, Minimal cogenerators over Osofsky and Camillo rings, preprint, 1993.
- Carl Faith and Pere Menal, A counter example to a conjecture of Johns, Proc. Amer. Math. Soc. 116 (1992), no. 1, 21–26. MR 1100651, DOI 10.1090/S0002-9939-1992-1100651-0
- Carl Faith and Pere Menal, The structure of Johns rings, Proc. Amer. Math. Soc. 120 (1994), no. 4, 1071–1081. MR 1231294, DOI 10.1090/S0002-9939-1994-1231294-8 C. Perelló (ed.), Pere Menal memorial volumes, Publ. Mat. 36 (1992).
Additional Information
- © Copyright 1995 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 123 (1995), 1635-1637
- MSC: Primary 16E50
- DOI: https://doi.org/10.1090/S0002-9939-1995-1254836-6
- MathSciNet review: 1254836