A homological characterization of Steinitz rings
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- by Helmut Lenzing PDF
- Proc. Amer. Math. Soc. 29 (1971), 269-271 Request permission
Abstract:
A ring R (associative with an identity) is called a right Steinitz ring if any linearly independent subset of a free right R-module F can be extended to a basis of F. Steinitz rings have been investigated in a recent paper of Chwe and Neggers. In this note it is shown that the right Steinitz rings are exactly the right perfect, local rings.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
- 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
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Additional Information
- © Copyright 1971 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 29 (1971), 269-271
- MSC: Primary 16.40
- DOI: https://doi.org/10.1090/S0002-9939-1971-0274503-9
- MathSciNet review: 0274503