The Lattice of Varieties of Implication Semigroups

Abstract

An implication semigroup is an algebra of type (2, 0) with a binary operation → and a 0-ary operation 0 satisfying the identities (x→ y) → z≈ x→ (y→ z) , (x→y)→z≈[(z′→x)→(y→z)′]′ and 0 ′′≈ 0 where u′ means u→ 0 for any term u. We completely describe the lattice of varieties of implication semigroups. It turns out that this lattice is non-modular and consists of 16 elements. © 2019, Springer Nature B.V.