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Some varieties of algebraic systems of type $((n), (m))$ $((n), (m))$

D. Phusanga

http://orcid.org/0000-0002-2771-2310

Department of Mathematics, Faculty of Science, Maejo University, Chiang mai, 50290, Thailand

E-mail Address: darapu@mju.ac.th

Corresponding author.

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and

J. Koppitz

Institute of Mathematics and Informatics Bulgarian, Academy of Sciences, Sofia, 1113, Bulgaria

E-mail Address: koppitz@math.bas.bg

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https://doi.org/10.1142/S1793557119500050Cited by:1 (Source: Crossref)

Abstract

In the present paper, we classify varieties of algebraic systems of the type $((n), (m))$ $((n), (m))$ , for natural numbers $n$ $n$ and $m$ $m$ , which are closed under particular derived algebraic systems. If we replace in an algebraic system the $n$ $n$ -ary operation by an $n$ $n$ -ary term operation and the $m$ $m$ -ary relation by the $m$ $m$ -ary relation generated by an $m$ $m$ -ary formula, we obtain a new algebraic system of the same type, which we call derived algebraic system. We shall restrict the replacement to so-called “linear” terms and atomic “linear” formulas, respectively.

Communicated by I. Chajda

Keywords:

AMSC: 03C05, 03C07, 08A05, 08A02

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