Discussiones Mathematicae General Algebra and Applications 22(1) (2002) 87-100
doi: 10.7151/dmgaa.1049

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EQUATIONAL BASES FOR WEAK MONOUNARY VARIETIES

 Grzegorz Bińczak

Institute of Mathematics, Warsaw University of Technology
pl. Politechniki 1, 00-661 Warszawa, Poland
e-mail: binczak@mini.pw.edu.pl

Abstract

It is well-known that every monounary variety of total algebras has one-element equational basis (see [5]). In my paper I prove that every monounary weak variety has at most 3-element equational basis. I give an example of monounary weak variety having 3-element equational basis, which has no 2-element equational basis.

Keywords: partial algebra, weak equation, weak variety, regular equation, regular weak equational theory, monounary algebras.

2000 AMS Mathematics Subject Classifications: 08A55, 08B05.

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Received 19 April 2002
Revised 2 July 2002