Representations of regular double Stone algebras: theory and applications

In this paper, we put together several Cayley-type Theorems variously scattered in the literature over the past four decades to prove some general theorems that encompass all of them under the unifying framework of regular double Stone algebras. Indeed, we propose a matrix presentation à la Ésik of regular double Stone algebras, and we show that such representation can be equivalently regarded as an algebra of actions on a Boolean algebra.