Magnifiers in Some Generalization of the Full Transformation Semigroups

Thananya Kaewnoi, Montakarn Petapirak and Ronnason Chinram
Additional contact information
Thananya Kaewnoi: Department of Mathematics and Statistics, Prince of Songkla University, Hat Yai, Songkhla 90110, Thailand
Montakarn Petapirak: Algebra and Applications Research Unit, Department of Mathematics and Statistics, Prince of Songkla University, Hat Yai, Songkhla 90110, Thailand
Ronnason Chinram: Algebra and Applications Research Unit, Department of Mathematics and Statistics, Prince of Songkla University, Hat Yai, Songkhla 90110, Thailand

Mathematics, 2020, vol. 8, issue 4, 1-11

Abstract: 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.

Keywords: magnifiers; magnifying elements; transformation semigroups; equivalence relations; partitions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/8/4/473/pdf (application/pdf)
https://www.mdpi.com/2227-7390/8/4/473/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:8:y:2020:i:4:p:473-:d:338986

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().