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Finite Intersections of Pid or Factorial Overrings

Published online by Cambridge University Press:  20 November 2018

D. D. Anderson  and
David F. Anderson
D. D. Anderson
Affiliation:
Department of Mathematics, The University of IowaIowa City, Iowa 52242
David F. Anderson
Affiliation:
Department of Mathematics, The University of TennesseeKnoxville, Tennessee 37996-1300
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Abstract

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In this paper we study when an integral domain is a finite intersection of PID or factorial overrings. We show that any Krull domain is the intersection of a PID and a field. We give several sufficient conditions for a Krull domain to be an intersection of two PID or factorial overrings.

Keywords

13G0513B9913A0513F0613F1013F15
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 28 , Issue 1 , 01 March 1985 , pp. 91 - 97
Copyright
Copyright © Canadian Mathematical Society 1985

References

1. Anderson, D.D. and Anderson, D.F., Locally factorial integral domains, J. Algebra 90 (1984), pp. 265–283.Google Scholar
2. Claborn, L., Specified relations in the ideal group, Michigan Math. J. 15 (1968), pp. 249—255.Google Scholar
3. Estes, D. and Ohm, J., Stable range in commutative rings, J. Algebra 7 (1967), pp. 343—362.Google Scholar
4. Fossum, R.M., The divisor class group of a Krull domain, Springer-Verlag, New York, 1973.Google Scholar
5. Gilmer, R., An embedding theorem for HCF-rings, Proc. Camb. Phil. Soc. 68 (1970), pp. 583–587.Google Scholar
6. Gilmer, R., Multiplicative ideal theory, Dekker, New York, 1972.Google Scholar
7. Grams, A.P., The distribution of prime ideals of a Dedekind domain, Bull. Austral. Math. Soc. 11 (1974), pp. 429–441.Google Scholar
8. le Riche, L. R., The ring R〈x〉, J. Algebra 67 (1980), pp. 327–341.Google Scholar