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Proceedings of the American Mathematical Society

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The regular element property

Author: Fred Richman
Journal: Proc. Amer. Math. Soc. 126 (1998), 2123-2129
MSC (1991): Primary 03F65, 13E05; Secondary 13P99, 13C15
MathSciNet review: 1443853
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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 [Enhancements On Off] (What's this?)

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  • 2. Kaplansky, Irving, Commutative rings, University of Chicago Press, 1974. MR 49:10674
  • 3. Mines, Ray, Fred Richman and Wim Ruitenburg, A course in constructive algebra, Springer-Verlag, 1988. MR 89d:03066
  • 4. Seidenberg, Abraham, Constructions in Algebra, Trans. Amer. Math. Soc. 197 (1974), 273-313. MR 50:2141

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Additional Information

Fred Richman
Affiliation: Department of Mathematics, Florida Atlantic University, Boca Raton, Florida 33431-0991

Received by editor(s): August 21, 1996
Received by editor(s) in revised form: December 17, 1996
Communicated by: Wolmer V. Vasconcelos
Article copyright: © Copyright 1998 American Mathematical Society