DM-GAA

ISSN 1509-9415 (print version)

ISSN 2084-0373 (electronic version)

https://doi.org/10.7151/dmgaa

Discussiones Mathematicae - General Algebra and Applications

Cite Score (2023): 0.6

SJR (2023): 0.214

SNIP (2023): 0.604

Index Copernicus (2022): 121.02

H-Index: 5

Discussiones Mathematicae - General Algebra and Applications

Article in volume

Authors:

A. Charoenpol

Aveya Charoenpol

Department of Mathematics, Faculty of Engineering
Rajamangala University of Technology Isan Khonkaen Campus
Thailand 40000

email: aveya.ch@rmuti.ac.th

Udom Chotwattakawanit

Udom Chotwattakawanit

Khon Kaen University

email: udomch@kku.ac.th

Title:

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

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Source:

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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