A multiplication of $e$-varieties of orthodox semigroups
Martin Kuřil · Czech digital mathematics library · 1995
. 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. 1. Introduction We will investigate here an operator on the lattice of all e--varieties of regular semigroups. We define semantically a partial multiplication on this lattice: U V is defined if U is an e--variety of regular semigroups and V is an e--variety of inverse semigroups. In the case that U is an e--variety of orthodox semigroups we can also describe our multiplication syntactically in terms of biinvariant congruences. The motivation for us was Pol#k's paper [5]. It deals with a multiplication on the lattice of varieties of -regular semigroups. The semantical definition is based on a certain semidirect product S \\Theta ' T , where S = (S; \\Delta; 0 ) is a -regular semigroup, T = (T; \\Delta; 0 ) is a locally inver...