Geodesic
The pre-period of the glued sum of finite modular lattices
Discussiones Mathematicae. General Algebra and Applications, Tome 43 (2023) no. 2, pp. 223-231

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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.
Keywords: ordinal sum, glued sum, modular lattice, endomorphism, pre-period, connected unary operation 
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Charoenpol, Aveya; Chotwattakawanit, Udom. The pre-period of the glued sum of finite modular lattices. Discussiones Mathematicae. General Algebra and Applications, Tome 43 (2023) no. 2, pp. 223-231. http://geodesic.mathdoc.fr/item/DMGAA_2023_43_2_a3/