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Proceedings of the American Mathematical Society

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

 

 

Semihereditary polynomial rings


Author: Victor P. Camillo
Journal: Proc. Amer. Math. Soc. 45 (1974), 173-174
MSC: Primary 16A30; Secondary 13F20
MathSciNet review: 0352165
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Abstract: It is shown that if the ring of polynomials over a commutative ring $ R$ is semihereditary then $ R$ is von Neumann regular. This is the converse of a theorem of P. J. McCarthy.


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DOI: https://doi.org/10.1090/S0002-9939-1974-0352165-2
Keywords: Von Neumann regular ring, semihereditary ring, distributive lattice
Article copyright: © Copyright 1974 American Mathematical Society