FUSIBLE RINGS

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.