This work reveals the structure of MPP monounary algebras via endomorphisms in finite modular lattices, highlighting their relationship with direct products and chains.
A finite modular lattice A is said to be MPP if there is an endomorphism, called an MPP endomorphism, whose the pre-period is equal to the length of A. A monounary algebra $(A,f)$ is said to be MPP if f is an MPP endomorphism of a lattice , 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.
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Charoenpol et al. (2025) studied this question.
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