Semihereditary polynomial rings

Camillo, Victor P.

doi:10.1090/S0002-9939-1974-0352165-2

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

Semihereditary polynomial rings
HTML articles powered by AMS MathViewer

by Victor P. Camillo PDF

Proc. Amer. Math. Soc. 45 (1974), 173-174 Request permission

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.

References

Victor P. Camillo, A note on semi-hereditary rings, Arch. Math. (Basel) 24 (1973), 142–143. MR 318135, DOI 10.1007/BF01228190
P. J. McCarthy, The ring of polynomial over a von Neumann regular ring, Proc. Amer. Math. Soc. 39 (1973), 253–254. MR 316496, DOI 10.1090/S0002-9939-1973-0316496-3