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.
| Identifer | oai:union.ndltd.org:unt.edu/info:ark/67531/metadc331394 |
| Date | 05 1900 |
| Creators | Race, Denise T. (Denise Tatsch) |
| Contributors | Vaughan, Nick H., Mohat, John T., 1924-, Lewis, Paul Weldon, Brand, Neal E. |
| Publisher | North Texas State University |
| Source Sets | University of North Texas |
| Language | English |
| Detected Language | English |
| Type | Thesis or Dissertation |
| Format | iii, 49 leaves, Text |
| Rights | Public, Race, Denise T. (Denise Tatsch), Copyright, Copyright is held by the author, unless otherwise noted. All rights reserved. |
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