On semihereditary noncommutative polynomial rings
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- by P. Pillay
- Proc. Amer. Math. Soc. 78 (1980), 473-474
- DOI: https://doi.org/10.1090/S0002-9939-1980-0556614-9
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Abstract:
McCarthy [4] showed that a polynomial ring over a commutative von Neumann regular ring is semihereditary. Camillo [1] proved the converse. In this paper we examine polynomial rings over von Neumann regular rings which are not necessarily commutative.References
- Victor P. Camillo, Semihereditary polynomial rings, Proc. Amer. Math. Soc. 45 (1974), 173–174. MR 352165, DOI 10.1090/S0002-9939-1974-0352165-2
- Carl Faith, Algebra: rings, modules and categories. I, Die Grundlehren der mathematischen Wissenschaften, Band 190, Springer-Verlag, New York-Heidelberg, 1973. MR 0366960
- Chr. U. Jensen, On homological dimensions of rings with countably generated ideals, Math. Scand. 18 (1966), 97–105. MR 207796, DOI 10.7146/math.scand.a-10784
- 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
Bibliographic Information
- © Copyright 1980 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 78 (1980), 473-474
- MSC: Primary 16A30
- DOI: https://doi.org/10.1090/S0002-9939-1980-0556614-9
- MathSciNet review: 556614