Next Article in Journal
Generalized 5-Point Approximating Subdivision Scheme of Varying Arity
Previous Article in Journal
The Derived Subgroups of Sylow 2-Subgroups of the Alternating Group, Commutator Width of Wreath Product of Groups
Open AccessArticle

Magnifiers in Some Generalization of the Full Transformation Semigroups

1
Department of Mathematics and Statistics, Prince of Songkla University, Hat Yai, Songkhla 90110, Thailand
2
Algebra and Applications Research Unit, Department of Mathematics and Statistics, Prince of Songkla University, Hat Yai, Songkhla 90110, Thailand
3
Centre of Excellence in Mathematics, CHE, Si Ayuthaya Road, Bangkok 10400, Thailand
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(4), 473; https://doi.org/10.3390/math8040473
Received: 7 February 2020 / Revised: 17 March 2020 / Accepted: 27 March 2020 / Published: 30 March 2020
(This article belongs to the Special Issue Algebra and Number Theory)
An element a of a semigroup S is called a left [right] magnifier if there exists a proper subset M of S such that a M = S ( M a = S ) . Let T ( X ) denote the semigroup of all transformations on a nonempty set X under the composition of functions, P = { X i i Λ } be a partition, and ρ be an equivalence relation on the set X. In this paper, we focus on the properties of magnifiers of the set T ρ ( X , P ) = { f T ( X ) ( x , y ) ρ , ( x f , y f ) ρ and X i f X i for all i Λ } , which is a subsemigroup of T ( X ) , and provide the necessary and sufficient conditions for elements in T ρ ( X , P ) to be left or right magnifiers. View Full-Text
Keywords: magnifiers; magnifying elements; transformation semigroups; equivalence relations; partitions magnifiers; magnifying elements; transformation semigroups; equivalence relations; partitions
MDPI and ACS Style

Kaewnoi, T.; Petapirak, M.; Chinram, R. Magnifiers in Some Generalization of the Full Transformation Semigroups. Mathematics 2020, 8, 473.

Show more citation formats Show less citations formats
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Search more from Scilit
 
Search
Back to TopTop