Date of Award

2017

Document Type

Dissertation/Thesis

Submission Date

October 2026

Thesis/Dissertation Advisor [Chair]

McGovern, Warren W.

Abstract

Abstract algebra is the study of structure, as represented by a set with operations acting on the set. One such type of structure is known as a ring. Rings themselves are abstract objects which may be classi ed. Such classi cations become a large area of study in ring theory. If every instance of a class of rings satis es the de ning property for another class and vice versa, then they are equivalient classi cations. However, if every instance of one class satis es the de ning property of the other ring, yet there is a counterexample of a ring that satis es the latter, but not the former, the latter ring is generalization of the former. In this thesis, we present a quick survey of foundational topics in abstract algebra, and discuss main results about von Neumann regular rings, complemented rings, and nally, fusible rings. We display a counstruction of a ring that is fusible, yet not complemented, thus concluding that the class of fusible rings is a generalization of the class of complemented rings.

Comments

Includes bibliography.

Extent

52 p.

Identifier

FA00012628

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