ABSTRACT
This chapter describes an important class of semigroup algebras arising from completely 0-simple semigroups. They are crucial for investigating “local” properties of arbitrary semigroup algebras. It briefly discusses a connection between the classes of modules over a Munn algebra, which exploits the mapping of complete semilattice embedding. The chapter presents an important auxiliary result providing necessary and sufficient conditions for a Munn algebra to have an identity. It provides a study of the structure of algebras of certain not necessarily completely 0-simple semigroups. Munn algebras appeared in a characterization of simple rings with minimal one-sided ideals as those algebras of matrix type over a division algebra D, the sandwich matrix of which has rows and columns left, respectively right, D-independent.
