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CPI-Extensions: Overrings of Integral Domains with Special Prime Spectrums

Published online by Cambridge University Press:  20 November 2018

Monte B. Boisen JR.  and
Philip B. Sheldon
Monte B. Boisen JR.
Affiliation:
Virginia Polytechnic Institute and State University, Blacksburg, Virginia
Philip B. Sheldon
Affiliation:
Virginia Polytechnic Institute and State University, Blacksburg, Virginia
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Throughout this paper the term ring will denote a commutative ring with unity and the term integral domain will denote a ring having no nonzero divisors of zero. The set of all prime ideals of a ring R can be viewed as a topological space, called the prime spectrum of R, and abbreviated Spec (R), where the topology used is the Zariski topology [1, Definition 4, § 4.3, p. 99]. The set of all prime ideals of R can also be viewed simply as aposet - that is, a partially ordered set - with respect to set inclusion. We will use the phrase the pospec of R, or just Pospec (/v), to refer to this partially ordered set.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 29 , Issue 4 , 01 August 1977 , pp. 722 - 737
Copyright
Copyright © Canadian Mathematical Society 1977

References

1. Bourbaki, Nicolas, Commutative algebra (Addison-Wesley Publishing Company, 1972).Google Scholar
2. Bastida, Eduardo and Gilmer, Robert, Over rings and divisorial ideals of rings of the form D + M, Mich. Math. J. 20 (1973), 79–95.Google Scholar
3. Boisen, Monte B., Jr. and Larsen, Max D., On Priifer rings as images of Priifer domains, Proc. Amer. Math. Soc. Ifl (1973), 87–90.Google Scholar
4. Boisen, Monte B., Jr. and Sheldon, Philip B., The valuation structure of hornomorphie images of Prilfer domains, Proc. Amer. Math. Soc. Ifi (1974), 335–342.Google Scholar
5. Boisen, Monte B. Pre-Priifer rings, Pac. J. Math. 58 (1975), 331–344.Google Scholar
6. Gilmer, Robert and Ohm, Jack, Primary ideals and valuation ideals. Trans. Amer. Math. Soc. 117 (1965), 237–250.Google Scholar
7. Hochster, M., Prime ideal structure in commutative rings, Trans. Amer. Math. Soc. 1J+2 (1969), 43–60.Google Scholar
8. Kaplansky, Irving, Commutative rings (revised edition) (University of Chicago Press, 1974).Google Scholar
9. Lang, Serge, Algebra (Addison-Wesley, 1971).Google Scholar
10. Larsen, Max D. and McCarthy, Paul J., Multiplicative theory of ideals (Academic Press, 1971).Google Scholar
11. Lewis, William J., The spectrum of a ring as a partially ordered set, J. Alg. 25 (1973), 419–434.Google Scholar
12. Masayoshi, Nagata, Local rings (Interscience, 1962).Google Scholar