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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
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:
- 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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MSC (1991):
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MSC (1991):
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Additional Information:
Fred
Richman
Affiliation:
Department of Mathematics, Florida Atlantic University, Boca Raton, Florida 33431-0991
Email:
richman@acc.fau.edu
DOI:
10.1090/S0002-9939-98-04257-9
PII:
S 0002-9939(98)04257-9
Received by editor(s):
August 21, 1996
Received by editor(s) in revised form:
December 17, 1996
Communicated by:
Wolmer V. Vasconcelos
Copyright of article:
Copyright
1998,
American Mathematical Society
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