A homological characterization of Steinitz rings-Reference-Cited by-同舟云学术

A homological characterization of Steinitz rings

Published:1971 Issue:2 Volume:29 Page:269-271
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Lenzing Helmut

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.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/1971-029-02/S0002-9939-1971-0274503-9/S0002-9939-1971-0274503-9.pdf

Reference4 articles.

1. Finitistic dimension and a homological generalization of semi-primary rings;Bass, Hyman;Trans. Amer. Math. Soc.,1960

2. On the extension of linearly independent subsets of free modules to bases;Chwe, Byoung-song;Proc. Amer. Math. Soc.,1970

3. Rings over which flat modules are free;Govorov, V. E.;Dokl. Akad. Nauk SSSR,1962

4. Projective modules;Kaplansky, Irving;Ann. of Math (2),1958

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