Kleene Algebrae, Kleene Modules, and Morita Equivalence

Modules and the notion of Morita equivalence are foundational to the classical study of rings. These concepts extend naturally to semirings and then specialize to Kleene algebrae, and my goal is to investigate Kleene modules and Morita equivalence of Kleene algebrae in the hope that some of the power seen in the context of rings may be found in this new context as well.