Finite Intersections of Pid or Factorial Overrings
Canadian mathematical bulletin, Tome 28 (1985) no. 1, pp. 91-97

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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.
DOI : 10.4153/CMB-1985-009-0
Mots-clés : 13G05, 13B99, 13A05, 13F06, 13F10, 13F15
Anderson, D. D.; Anderson, David F. Finite Intersections of Pid or Factorial Overrings. Canadian mathematical bulletin, Tome 28 (1985) no. 1, pp. 91-97. doi: 10.4153/CMB-1985-009-0
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[1] 1. Anderson, D.D. and Anderson, D.F., Locally factorial integral domains, J. Algebra 90 (1984), pp. 265–283. Google Scholar

[2] 2. Claborn, L., Specified relations in the ideal group, Michigan Math. J. 15 (1968), pp. 249—255. Google Scholar

[3] 3. Estes, D. and Ohm, J., Stable range in commutative rings, J. Algebra 7 (1967), pp. 343—362. Google Scholar

[4] 4. Fossum, R.M., The divisor class group of a Krull domain, Springer-Verlag, New York, 1973. Google Scholar

[5] 5. Gilmer, R., An embedding theorem for HCF-rings, Proc. Camb. Phil. Soc. 68 (1970), pp. 583–587. Google Scholar

[6] 6. Gilmer, R., Multiplicative ideal theory, Dekker, New York, 1972. Google Scholar

[7] 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] 8. le Riche, L. R., The ring R〈x〉, J. Algebra 67 (1980), pp. 327–341. Google Scholar

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