On sandwich semigroups in Boolean group algebras

Let BG be a Boolean group algebra, and let R be a nonzero element in BG, where G is an abelian group of order n. The sandwich semigroup of BG with a sandwich element R is denoted by BG(R). The purpose of this paper is to discuss Greenʹs classes, idempotent elements, regular elements, and maximal subgroups for BG(R), and apply the obtained results to Boolean matrices.