The pre-period of the glued sum of finite modular lattices

Abstract

The notion of a pre-period of an algebra A is defined by means of the notion of the pre-period λ(f ) of a monounary algebra A; f : it is determined by sup{λ(f ) | f is an endomorphism of A}. In this paper we focus on the pre-period of a finite modular lattice. The main result is that the pre-period of any finite modular lattice is less than or equal to the length of the lattice; also, necessary and sufficient conditions under which the pre-period of the glued sum is equal to the length of the lattice, are shown. Moreover, we show the triangle inequality of the pre-period of the glued sum.