DM-GAA

Article in volume

Authors:

Y.L. Tenkeu Jeufack

Y.L. Tenkeu Jeufack

Department of Mathematics
Ecole Normale Supérieure
University of Yaoundé-1
P.O. Box 47 Yaoundé Cameroon

email: ytenkeu2018@gmail.com

J. Djoumessi

Joseph Djoumessi

Department of Mathematics
Ecole Normale Supérieure
University of Yaoundé-1
P.O. Box 47 Yaoundé Cameroon

email: joseph.djoumessi@yahoo.fr

E.R. Temgoua Alomo

Etienne R. Temgoua Alomo

Department of Mathematics
École Normale Supérieure de Yaoundé, University of Yaoundé 1
P.O. Box 47, Yaoundé, Cameroon

email: retemgoua@yahoo.fr

Title:

Binary relations and submaximal clones determined by central relation

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Source:

Discussiones Mathematicae - General Algebra and Applications 43(2) (2023) 263-300

Received: 2021-10-07 , Revised: 2022-04-13 , Accepted: 2022-04-13 , Available online: 2023-01-13 , https://doi.org/10.7151/dmgaa.1423

Abstract:

Let $\rho$ be an $h$-ary central relation ($h\geq 2$) and $\sigma$ a binary relation on a finite set $A$ such that $\sigma\neq\rho$. It is known from Rosenberg's classification theorem (1965) that the clone $\textrm{ Pol} \rho$ which consists of all operations on $A$ that preserve $\rho$ is a maximal clone on $A$. In this paper, we find all binary relations $\sigma$ such that the clone $\textrm{Pol} \{\rho, \sigma\}$ is a maximal subclone of $\textrm{Pol} \rho$, where $\rho$ is a fixed central relation.

Keywords:

central relations, meet-reducible, meet-irreducible, submaximal, clones

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