Semihereditary polynomial rings
Author:
Victor P. Camillo
Journal:
Proc. Amer. Math. Soc. 45 (1974), 173-174
MSC:
Primary 16A30; Secondary 13F20
DOI:
https://doi.org/10.1090/S0002-9939-1974-0352165-2
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.
- Victor P. Camillo, A note on semi-hereditary rings, Arch. Math. (Basel) 24 (1973), 142–143. MR 318135, DOI https://doi.org/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 https://doi.org/10.1090/S0002-9939-1973-0316496-3
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Keywords:
Von Neumann regular ring,
semihereditary ring,
distributive lattice
Article copyright:
© Copyright 1974
American Mathematical Society
