IJPAM: Volume 87, No. 1 (2013)
WITH INVARIANT SETS
1,2,3Department of Mathematics
Faculty of Science
Chiang Mai University
Chiangmai, 50200, THAILAND
Abstract. Let be the semigroup of all transformations on a set . For a fixed nonempty subset of , let
Then is a semigroup of total transformations on which leave a subset of invariant. In this paper, we characterize left regular, right regular and intra-regular elements of and consider the relationships between these elements. Moreover, we count the number of left regular elements of when is a finite set.
Received: June 4, 2013
AMS Subject Classification: 20M20
Key Words and Phrases: transformation semigroups, left regular element, right regular element, intra-regular element
Download paper from here.
DOI: 10.12732/ijpam.v87i1.9 How to cite this paper?
Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395