  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 [8] which led Sankappanavar to introduce, and investigate, the
variety I of implication zroupoids generalizing De Morgan algebras. His
investigations were continued in [3] and [4] in which several new subvarieties
of I were introduced and their relationships with each other and with the
varieties of [8] were explored. The present paper is a continuation of [8] and
[3]. The main purpose of this paper is to determine the simple algebras in I.
It is shown that there are exactly five simple algebras in I. From this
description we deduce that the semisimple subvarieties of I are precisely the
subvarieties of the variety generated by these 5 simple I-zroupoids and are
locally finite. It also follows that the lattice of semisimple subvarieties of
I is isomorphic to the direct product of a 4-element Boolean lattice and a
4-element chain.
