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Proceedings of the American Mathematical Society

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

 

 

Projective modules over rings with many units


Authors: B. R. McDonald and William C. Waterhouse
Journal: Proc. Amer. Math. Soc. 83 (1981), 455-458
MSC: Primary 13C10; Secondary 13B25
DOI: https://doi.org/10.1090/S0002-9939-1981-0627668-7
MathSciNet review: 627668
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Abstract: Let $ R$ be a commutative ring. Assume that every polynomial whose values generate the unit ideal actually takes on an invertible value. Then projective $ R$-modules split into cyclic summands, and those of constant rank are free.


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DOI: https://doi.org/10.1090/S0002-9939-1981-0627668-7
Article copyright: © Copyright 1981 American Mathematical Society