A Galois correspondence for universal algebras
We present a groupoid which can be converted into a Boolean algebra with respect to term operations. Also conversely, every Boolean algebra can be reached in this way.
We define semantically a partial multiplication on the lattice of all e–varieties of regular semigroups. In the case that the first factor is an e–variety of orthodox semigroups we describe our multiplication syntactically in terms of biinvariant congruences.
A multiplication of e-varieties of regular -solid semigroups by inverse semigroup varieties is described both semantically and syntactically. The associativity of the multiplication is also proved.