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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 homological characterization of Steinitz rings


Author: Helmut Lenzing
Journal: Proc. Amer. Math. Soc. 29 (1971), 269-271
MSC: Primary 16.40
MathSciNet review: 0274503
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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.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1971-0274503-9
PII: S 0002-9939(1971)0274503-9
Keywords: Perfect ring, local ring, Steinitz ring, linearly independent subset, basis, finitistic projective dimension
Article copyright: © Copyright 1971 American Mathematical Society