An MPP Monounary Algebra Induced by an Endomorphism of the Direct Product of Two Chains

A finite modular lattice $\mathbf{A}$ is said to be \textit{MPP} if there is an endomorphism, called an\textit{ MPP endomorphism}, whose the pre-period is equal to the length of $\mathbf{A}$. A monounary algebra $(A,f)$ is said to be \textit{MPP} if $f$ is an MPP endomorphism of a lattice $\A$, called an MPP corresponding lattice to $(A,f)$. In this work, we show all MPP monounary algebras induced by endomorphisms of the direct products of two chains.