Some Studies On Power Semigroups

If S is a semigroup, the power semigroup (or the global) of S is the set Р(S) of all nonempty subsets of S equipped with a naturally defined multiplication. A class К of semigroups is globally determined if any two semigroups of К with isomorphic globals are themselves isomorphic.In this dissertation, we study globals of normal orthogroups (i.e., strong semilattices of rectangular groups) and globals of idempotent semigroups (i.e., bands), and show, in particular, that the class of normal orthogroups and the class of semigroups with regular globals are globally determined.