Czechoslovak Mathematical Journal, Vol. 57, No. 2, pp. 573-578, 2007

Subdirect products of certain varieties of
unary algebras

M. Ciric, T. Petkovic, S. Bogdanovic

Miroslav Ciric, Faculty of Sciences and Mathematics, University of Nis, Visegradska 33, P. O. Box 224, 18000 Nis, Serbia, e-mail: ciricm@bankerinter.net; Tatjana Petkovic, Academy of Finland and Department of Information Technology, University of Turku, FIN-20014 Turku, Finland, e-mail: tatpet@utu.fi; Stojan Bogdanovic, Faculty of Economics, University of Nis, Trg Kralja Aleksandra 11, P. O. Box 121, 18000 Nis, Serbia, e-mail: sbogdan@pmf.ni.ac.yu

Abstract: J. Plonka in [12] noted that one could expect that the regularization ${\Cal R}(\bk K)$ of a variety ${\bk K}$ of unary algebras is a subdirect product of ${\bk K}$ and the variety ${\bk D}$ of all discrete algebras (unary semilattices), but is not the case. The purpose of this note is to show that his expectation is fulfilled for those and only those irregular varieties ${\bk K}$ which are contained in the generalized variety $\TDir$ of the so-called trap-directable algebras.

Keywords: unary algebra, subdirect product, variety, directable algebra

Classification (MSC 2000): 08A60, 08B26, 08B15, 08A70


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