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Containment Relations Between Classes of Regular Ideals in a Ring with Few Zero Divisors

This dissertation focuses on the significance of containment relations between the above mentioned classes of ideals. The main problem considered in Chapter II is determining conditions which lead a ring to be a P-ring, D-ring, or AM-ring when every regular ideal is a P-ideal, D-ideal, or AM-ideal, respectively. We also consider containment relations between classes of regular ideals which guarantee that the ring is a quasi-valuation ring. We continue this study into the third chapter; in particular, we look at the conditions in a quasi-valuation ring which lead to a = Jr, sr - f, and a = v. Furthermore we give necessary and sufficient conditions that a ring be a discrete rank one quasi-valuation ring. For example, if R is Noetherian, then ft = J if and only if R is a discrete rank one quasi-valuation ring.

Identiferoai:union.ndltd.org:unt.edu/info:ark/67531/metadc331394
Date05 1900
CreatorsRace, Denise T. (Denise Tatsch)
ContributorsVaughan, Nick H., Mohat, John T., 1924-, Lewis, Paul Weldon, Brand, Neal E.
PublisherNorth Texas State University
Source SetsUniversity of North Texas
LanguageEnglish
Detected LanguageEnglish
TypeThesis or Dissertation
Formatiii, 49 leaves, Text
RightsPublic, Race, Denise T. (Denise Tatsch), Copyright, Copyright is held by the author, unless otherwise noted. All rights reserved.

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