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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

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