Left perfect rings that are right perfect and a characterization of Steinitz rings
HTML articles powered by AMS MathViewer
- by William H. Rant PDF
- Proc. Amer. Math. Soc. 32 (1972), 81-84 Request permission
Abstract:
A proof is given to show all flat left modules of a ring are free if and only if the ring is a local ring with a left T-nilpotent maximal ideal. We characterize left perfect rings whose radical R has the property that $I{R^n} = \{ 0\}$ for some positive integer n if I is a finitely generated right ideal contained in R. We cite an example of a left perfect ring which does not have this property. It is shown that if the set of irreducible elements of a left perfect ring is right T-nilpotent then the ring is right perfect.References
- Hyman Bass, Finitistic dimension and a homological generalization of semi-primary rings, Trans. Amer. Math. Soc. 95 (1960), 466–488. MR 157984, DOI 10.1090/S0002-9947-1960-0157984-8
- Jan-Erik Björk, Rings satisfying a minimum condition on principal ideals, J. Reine Angew. Math. 236 (1969), 112–119. MR 248165, DOI 10.1515/crll.1969.236.112
- Byoung-song Chwe and Joseph Neggers, On the extension of linearly independent subsets of free modules to bases, Proc. Amer. Math. Soc. 24 (1970), 466–470. MR 252432, DOI 10.1090/S0002-9939-1970-0252432-3
- V. E. Govorov, Rings over which flat modules are free, Dokl. Akad. Nauk SSSR 144 (1962), 965–967 (Russian). MR 0139645
- B. L. Osofsky, A generalization of quasi-Frobenius rings, J. Algebra 4 (1966), 373–387. MR 204463, DOI 10.1016/0021-8693(66)90028-7
Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 32 (1972), 81-84
- MSC: Primary 16.50
- DOI: https://doi.org/10.1090/S0002-9939-1972-0289571-9
- MathSciNet review: 0289571