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

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Description

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 ... continued below

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iii, 49 leaves

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Race, Denise T. (Denise Tatsch) May 1987.

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  • Race, Denise T. (Denise Tatsch)

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Description

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.

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iii, 49 leaves

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  • May 1987

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  • Aug. 22, 2014, 6 p.m.

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  • March 21, 2016, 10:27 a.m.

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Race, Denise T. (Denise Tatsch). Containment Relations Between Classes of Regular Ideals in a Ring with Few Zero Divisors, dissertation, May 1987; Denton, Texas. (digital.library.unt.edu/ark:/67531/metadc331394/: accessed November 18, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; .