# A Proof Of Ore's Theorem

- ASU Author/Contributor (non-ASU co-authors, if there are any, appear on document)
- Linda Charlene Graham Madison (Creator)
- Institution
- Appalachian State University (ASU )
- Web Site: https://library.appstate.edu/
- Advisor
- L. Perry

**Abstract:** The classical construction of the rational numbers involves consideration of certain equivalence classes of ordered pairs [(a,b)] where a and b are integers with b nonzero. An elementary generalization of this idea is Ore's Theorem which gives a necessary and sufficient condition that a ring, not necessarily commutative and not necessarily a domain of integrity, can be extended to a ring of "fractions." The purpose of this thesis is to analyze another proof of Ore's Theorem which involves a bare minimum of technique using the method of maximal extensions of semi-endomorphisms defined on a certain class of right ideals, i.e., given a ring with Ore's Condition we will construct the classical ring of right quotients.

A Proof Of Ore's Theorem

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Created on 8/16/2021

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## Additional Information

- Publication
- Thesis
- Madison, L. (1973). A Proof Of Ore's Theorem. Unpublished Masterâ€™s Thesis. Appalachian State University, Boone, NC.
- Language: English
- Date: 1973
- Keywords
- mathematics, mathematical sciences, Ore's Theorem, fractions, nonzero

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