  The variety $\mathbf{I}$ of implication zroupoids was defined and
investigated by Sankappanavar ([7]) as a generalization of De Morgan algebras.
Also, in [7], several new subvarieties of $\mathbf{I}$ were introduced,
including the subvariety $\mathbf{I_{2,0}}$, defined by the identity: $x"
\approx x$, which plays a crucial role in this paper. Several more new
subvarieties of $\mathbf{I}$, including the subvariety $\mathbf{SL}$ of
semilattices with a least element $0$, are studied in [3], and an explicit
description of semisimple subvarieties of $\mathbf{I}$ is given in [5].
  It is well known that the operation $\land$ induces a partial order
($\sqsubseteq$) in the variety $\mathbf{SL}$ and also in the variety
$\mathbf{DM}$ of De Morgan algebras. As both $\mathbf{SL}$ and $\mathbf{DM}$
are subvarieties of $\mathbf{I}$ and the definition of partial order can be
expressed in terms of the implication and the constant, it is but natural to
ask whether the relation $\sqsubseteq$ (now defined) on $\mathbf{I}$ is
actually a partial order in some (larger) subvariety of $\mathbf{I}$ that
includes $\mathbf{SL}$ and $\mathbf{DM}$.
  The purpose of the present paper is two-fold: Firstly, a complete answer is
given to the above mentioned problem. Indeed, our first main theorem shows that
the variety $\mathbf{I_{2,0}}$ is a maximal subvariety of $\mathbf{I}$ with
respect to the property that the relation $\sqsubseteq$ is a partial order on
its members. In view of this result, one is then naturally led to consider the
problem of determining the number of non-isomorphic algebras in
$\mathbf{I_{2,0}}$ that can be defined on an $n$-element chain (herein called
$\mathbf{I_{2,0}}$-chains), $n$ being a natural number. Secondly, we answer
this problem in our second main theorem, which says that, for each $n \in
\mathbb{N}$, there are exactly $n$ nonisomorphic $\mathbf{I_{2,0}}$-chains of
size $n$.
