Title :
On Endoprimal Monoids in Clone Theory
Author :
Machida, Hajime ; Rosenberg, Ivo G.
Author_Institution :
Dept. of Math., Hitotsubashi Univ., Tokyo
Abstract :
The endomorphisms of a universal algebra on a universe A form a monoid of selfmaps on A. Such monoids, called endoprimal monoids, are special and rare. In this paper we study the first interesting case of a 3-element set A. In the lattice of inclusion-ordered endoprimal monoids we find three maximal endoprimal monoids. This knowledge allows us to conclude that many large monoids are not endoprimal.
Keywords :
group theory; clone theory; lattice of inclusion-ordered endoprimal monoids; universal algebra; Algebra; Cloning; Lattices; Logic; Machinery; centralizer; clone; endoprimal monoid;
Conference_Titel :
Multiple-Valued Logic, 2009. ISMVL '09. 39th International Symposium on
Conference_Location :
Naha, Okinawa
Print_ISBN :
978-1-4244-3841-9
Electronic_ISBN :
0195-623X
DOI :
10.1109/ISMVL.2009.53
