On Magnifying Elements in E-Preserving Partial Transformation Semigroups

Thananya Kaewnoi, Montakarn Petapirak, Ronnason Chinram
2018 Mathematics  
Let S be a semigroup. An element a of S is called a right [left] magnifying element if there exists a proper subset M of S satisfying S = M a [ S = a M ] . Let E be an equivalence relation on a nonempty set X. In this paper, we consider the semigroup P ( X , E ) consisting of all E-preserving partial transformations, which is a subsemigroup of the partial transformation semigroup P ( X ) . The main propose of this paper is to show the necessary and sufficient conditions for elements in P ( X ,
more » ... lements in P ( X , E ) to be right or left magnifying.
doi:10.3390/math6090160 fatcat:ddc5fvlvnrhvtn5wqrmohpxgsq