Some Results on the Centralizers of Monoids in Clone Theory

Hajime Machida; Masahiro Miyakawa; Ivo G. Rosenberg

doi:10.1109/ISMVL.2002.1011063

Proceedings 32nd IEEE International Symposium on Multiple-Valued Logic

Some Results on the Centralizers of Monoids in Clone Theory

Year: 2002, Pages: 10

DOI Bookmark: 10.1109/ISMVL.2002.1011063

Authors

Hajime Machida, Hitotsubashi University
Masahiro Miyakawa, Tsukuba College of Technology
Ivo G. Rosenberg, Université de Montréal

Abstract

For a set

S

$S$ of multi-variable operations on a

k

$k$ -element set, the centralizer

S^{*}

$S^*$ is the set of operations which commute with all operations in

S

$S$ . In this paper we concentrate on monoids of unary operations and centralizers of such monoids. In the course of discussion the Kuznetsov criterion is effectively used. First we study such monoids whose centralizer is the trivial (least) clone

J_{k}

${\cal J}_k$ . Next we prove that the trivial monoid {id} is the only monoid whose centralizer is the clone of all operations. We also show that the centralizer of every (non-trivial) monoid is included in maximal clones of some specific kinds.

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Some Results on the Centralizers of Monoids in Clone Theory

Authors

Abstract

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