Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Regular modules


Author: David J. Fieldhouse
Journal: Proc. Amer. Math. Soc. 32 (1972), 49-51
MSC: Primary 16A64
DOI: https://doi.org/10.1090/S0002-9939-1972-0292882-4
MathSciNet review: 0292882
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Pierce [3] has shown that over a commutative regular ring every finitely generated submodule of an n-generated module is n-generated, and then has asked if this result holds for noncommutative regular rings. Here the result is shown for regular modules over any associative ring, which answers Pierce's question since a ring is regular if and only if every module is regular.


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


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 16A64

Retrieve articles in all journals with MSC: 16A64


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0292882-4
Keywords: Regular module, regular ring, pure submodule, n-generated module
Article copyright: © Copyright 1972 American Mathematical Society

American Mathematical Society