Article in volume
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Title:
The pre-period of the glued sum of finite modular lattices
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Discussiones Mathematicae - General Algebra and Applications 43(2) (2023) 223-231
Received: 2021-11-30 , Revised: 2021-12-13 , Accepted: 2022-01-04 , Available online: 2023-01-11 , https://doi.org/10.7151/dmgaa.1420
Abstract:
The notion of a pre-period of an algebra $\mathbf{A}$ is defined by means of
the notion of the pre-period $\lambda(f)$ of a monounary algebra $\langle A;f\rangle$:
it is determined by $\sup\{\lambda(f)| f$ is an endomorphism of $\mathbf{A}\}$. 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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