On a Class of Subsemigroup Lattices

Abstract

Under study is the structure of subsemigroup lattices of semigroups of elementary types. We establish that the subsemigroup lattices of semigroups of elementary types are lattice-universal. Also, we show that, for a series of classes $ {\mathbf{K}} $ of algebraic structures, each subsemigroup lattice of the semigroup of elementary types of the structures from $ {\mathbf{K}} $ contains the ideal lattice of a free lattice of countable rank as a sublattice.