The variety I\documentclass[12pt]{minimal}
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\begin{document}$${\mathbf{I}}$$\end{document} of implication zroupoids (using a binary operation →\documentclass[12pt]{minimal}
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\begin{document}$${\to}$$\end{document} and a constant 0) was defined and investigated by Sankappanavar (Scientia Mathematica Japonica 75(1):21–50, 2012), as a generalization of De Morgan algebras. Also, in Sankappanavar (Scientia Mathematica Japonica 75(1):21–50, 2012), several subvarieties of I\documentclass[12pt]{minimal}
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\begin{document}$${\mathbf{I}}$$\end{document} were introduced, including the subvariety I2,0\documentclass[12pt]{minimal}
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\begin{document}$${\mathbf{I_{2,0}}}$$\end{document}, defined by the identity: x″≈x\documentclass[12pt]{minimal}
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\begin{document}$${x^{\prime \prime}\approx x}$$\end{document}, which plays a crucial role in this paper. Some more new subvarieties of I\documentclass[12pt]{minimal}
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\begin{document}$${\mathbf{I}}$$\end{document} are studied in Cornejo and Sankappanavar (Algebra Univ, 2015) that includes the subvariety SL\documentclass[12pt]{minimal}
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\begin{document}$${\mathbf{SL}}$$\end{document} of semilattices with a least element 0. An explicit description of semisimple subvarieties of I\documentclass[12pt]{minimal}
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\begin{document}$${\mathbf{I}}$$\end{document} is given in Cornejo and Sankappanavar (Soft Computing, 2015). It is a well known fact that there is a partial order (denote it by ⊑\documentclass[12pt]{minimal}
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\begin{document}$${\sqsubseteq}$$\end{document}) induced by the operation ∧, both in the variety SL\documentclass[12pt]{minimal}
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\begin{document}$${\mathbf{SL}}$$\end{document} of semilattices with a least element and in the variety DM\documentclass[12pt]{minimal}
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\begin{document}$${\mathbf{DM}}$$\end{document} of De Morgan algebras. As both SL\documentclass[12pt]{minimal}
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\begin{document}$${\mathbf{SL}}$$\end{document} and DM\documentclass[12pt]{minimal}
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\begin{document}$${\mathbf{DM}}$$\end{document} are subvarieties of I\documentclass[12pt]{minimal}
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\begin{document}$${\mathbf{I}}$$\end{document} 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 ⊑\documentclass[12pt]{minimal}
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\begin{document}$${\sqsubseteq}$$\end{document} on I\documentclass[12pt]{minimal}
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\begin{document}$${\mathbf{I}}$$\end{document} is actually a partial order in some (larger) subvariety of I\documentclass[12pt]{minimal}
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\begin{document}$${\mathbf{I}}$$\end{document} that includes both SL\documentclass[12pt]{minimal}
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\begin{document}$${\mathbf{SL}}$$\end{document} and DM\documentclass[12pt]{minimal}
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\begin{document}$${\mathbf{DM}}$$\end{document}. 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 I2,0\documentclass[12pt]{minimal}
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\begin{document}$${\mathbf{I_{2,0}}}$$\end{document} is a maximal subvariety of I\documentclass[12pt]{minimal}
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\begin{document}$${\mathbf{I}}$$\end{document} with respect to the property that the relation ⊑\documentclass[12pt]{minimal}
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\begin{document}$${\sqsubseteq}$$\end{document} 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 I2,0\documentclass[12pt]{minimal}
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\begin{document}$${\mathbf{I_{2,0}}}$$\end{document} that can be defined on an n-element chain (herein called I2,0\documentclass[12pt]{minimal}
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\begin{document}$${\mathbf{I_{2,0}}}$$\end{document}-chains), n being a natural number. Secondly, we answer this problem in our second main theorem which says that, for each n∈N\documentclass[12pt]{minimal}
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\begin{document}$${n \in \mathbb{N}}$$\end{document}, there are exactly n nonisomorphic I2,0\documentclass[12pt]{minimal}
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\begin{document}$${\mathbf{I_{2,0}}}$$\end{document}-chains of size n.
