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Proceedings of the American Mathematical Society

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

 

 

Modules over semihereditary Bezout rings


Author: Thomas S. Shores
Journal: Proc. Amer. Math. Soc. 46 (1974), 211-213
MSC: Primary 13F10
DOI: https://doi.org/10.1090/S0002-9939-1974-0349663-4
MathSciNet review: 0349663
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Abstract: It is shown that every commutative semihereditary Bezout ring of Krull dimension at most one is an elementary divisor ring. A consequence is that the ring of polynomials in one indeterminate over a von Neumann regular ring is an elementary divisor ring.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1974-0349663-4
Keywords: Commutative von Neumann regular ring, polynomial ring, semihereditary ring, Hermite ring, Bezout ring, elementary divisor ring
Article copyright: © Copyright 1974 American Mathematical Society