Semihereditary polynomial rings

Camillo, Victor P.

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

Proceedings of the American Mathematical Society

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Semihereditary polynomial rings
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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