The maximum pre-period property of the direct product of chains

Abstract

The pre-period of a finite algebra is the maximum pre-period of its endomorphisms. We know that the pre-period of any finite modular lattice is less than or equal to the length of the lattice. A finite modular lattice is said to have the maximum pre-period property (MPP) if its pre-period and its length are equal. In this paper, we study MPP of the direct product of chains.