Implication Zroupoids I

Juan M. Cornejo, Hanamantagouda P. Sankappanavar

Published 2015-09-12Version 1

It is a well known fact that Boolean algebras can be defined using only implication and a constant. In 2012, this result was extended to De Morgan algebras in [11] which led Sankappanavar to introduce, and investigate, the variety I of implication zroupoids (I- zroupoids) generalizing De Morgan algebras. The present paper, a continuation of [11], is devoted to investigating the structure of the lattice of subvarieties of I, and also to making further contributions to the theory of implication zroupoids. Several new subvarieties of I are introduced and their relationships with each other and with the subvarieties of I, which were investigated in [11], are explored.