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The regular element property

Author(s): Fred Richman
Journal: Proc. Amer. Math. Soc. 126 (1998), 2123-2129.
MSC (1991): Primary 03F65, 13E05; Secondary 13P99, 13C15
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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:

1.: Bishop, Errett, Foundations of constructive analysis, McGraw-Hill, 1967. MR 36:4930
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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