Properties of Some Classical Integral Domains

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Description

Greatest common divisor domains, Bezout domains, valuation rings, and Prüfer domains are studied. Chapter One gives a brief introduction, statements of definitions, and statements of theorems without proof. In Chapter Two theorems about greatest common divisor domains and characterizations of Bezout domains, valuation rings, and Prüfer domains are proved. Also included are characterizations of a flat overring. Some of the results are that an integral domain is a Prüfer domain if and only if every overring is flat and that every overring of a Prüfer domain is a Prüfer domain.

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iii, 35 leaves

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Crawford, Timothy B. May 1975.

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This thesis is part of the collection entitled: UNT Theses and Dissertations and was provided by the UNT Libraries to the UNT Digital Library, a digital repository hosted by the UNT Libraries. It has been viewed 45 times. More information about this thesis can be viewed below.

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  • Crawford, Timothy B.

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Greatest common divisor domains, Bezout domains, valuation rings, and Prüfer domains are studied. Chapter One gives a brief introduction, statements of definitions, and statements of theorems without proof. In Chapter Two theorems about greatest common divisor domains and characterizations of Bezout domains, valuation rings, and Prüfer domains are proved. Also included are characterizations of a flat overring. Some of the results are that an integral domain is a Prüfer domain if and only if every overring is flat and that every overring of a Prüfer domain is a Prüfer domain.

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iii, 35 leaves

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  • May 1975

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  • June 24, 2015, 9:39 a.m.

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  • Aug. 10, 2016, 10:18 p.m.

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Crawford, Timothy B. Properties of Some Classical Integral Domains, thesis, May 1975; Denton, Texas. (https://digital.library.unt.edu/ark:/67531/metadc663731/: accessed July 18, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; .

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