Title :
Centralizing Monoids on a Three-Element Set
Author :
Machida, Hajime ; Rosenberg, Ivo G.
Author_Institution :
Grad. Sch. of Arts & Sci., Int. Christian Univ., Mitaka, Japan
Abstract :
Let A be a finite set with |A|>; 1. A centralizing monoid on A is a set of unary functions defined on A which commute with some set of (multi-variable) functions on A. In this paper we consider the case where A is a three-element set. Using the concept of a witness and Kuznetsov criterion, we determine all centralizing monoids on a three-element set. There are 192 centralizing monoids, which are divided into 48 conjugate classes.
Keywords :
group theory; multivalued logic; Kuznetsov criterion; centralizing monoids; conjugate class; finite set; multivariable function; three-element set; unary function; Abstracts; Algebra; Art; Cloning; Educational institutions; Equations; Frequency modulation; centralizer; centralizing monoid; clone;
Conference_Titel :
Multiple-Valued Logic (ISMVL), 2012 42nd IEEE International Symposium on
Conference_Location :
Victoria, BC
Print_ISBN :
978-1-4673-0908-0
DOI :
10.1109/ISMVL.2012.50
