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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.

References [Enhancements On Off] (What's this?)

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  • [2] B.-S. Chwe and J. Neggers, On the extension of linearly independent subsets of free modules to bases, Proc. Amer. Math. Soc. 24 (1970), 466-470. MR 40 #5652. MR 0252432 (40:5652)
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Keywords: Perfect ring, local ring, Steinitz ring, linearly independent subset, basis, finitistic projective dimension
Article copyright: © Copyright 1971 American Mathematical Society

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