The regular element property
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- by Fred Richman
- Proc. Amer. Math. Soc. 126 (1998), 2123-2129
- DOI: https://doi.org/10.1090/S0002-9939-98-04257-9
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Abstract:
The property that an ideal whose annihilator is zero contains a regular element is examined from the point of view of constructive mathematics. It is shown that this property holds for finitely presented algebras over discrete fields, and for coherent, Noetherian, strongly discrete rings that contain an infinite field.References
- Errett Bishop, Foundations of constructive analysis, McGraw-Hill Book Co., New York-Toronto-London, 1967. MR 0221878
- Irving Kaplansky, Commutative rings, Revised edition, University of Chicago Press, Chicago, Ill.-London, 1974. MR 0345945
- Ray Mines, Fred Richman, and Wim Ruitenburg, A course in constructive algebra, Universitext, Springer-Verlag, New York, 1988. MR 919949, DOI 10.1007/978-1-4419-8640-5
- A. Seidenberg, Constructions in algebra, Trans. Amer. Math. Soc. 197 (1974), 273–313. MR 349648, DOI 10.1090/S0002-9947-1974-0349648-2
Bibliographic Information
- Fred Richman
- Affiliation: Department of Mathematics, Florida Atlantic University, Boca Raton, Florida 33431-0991
- Email: richman@acc.fau.edu
- Received by editor(s): August 21, 1996
- Received by editor(s) in revised form: December 17, 1996
- Communicated by: Wolmer V. Vasconcelos
- © Copyright 1998 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 126 (1998), 2123-2129
- MSC (1991): Primary 03F65, 13E05; Secondary 13P99, 13C15
- DOI: https://doi.org/10.1090/S0002-9939-98-04257-9
- MathSciNet review: 1443853