Cleavability in Semigroups

In this thesis, the concept of cleavability as it applies to semigroups is explored. We will consider several results in which certain properties of semigroups are transferred by way of special homomorphisms. Much of our work focuses on a specialized form of cleavability called pointwise cleavability. The concept of cleavability was first studied in topology. Since its introduction, this property has been found to have implications in abstract algebra as well. Results in this thesis are based on an article written by D.J. Marron and T.B.M. McMaster in 2000. Details of proofs that were omitted in the article will be provided here, and new results, questions, and conjectures will be presented