Left (Right) Regular Elements of Some Transformation Semigroups

Kitsanachai Sripon, Ekkachai Laysirikul () and Worachead Sommanee
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Kitsanachai Sripon: Department of Mathematics, Faculty of Science, Naresaun University, Phitsanulok 65000, Thailand
Ekkachai Laysirikul: Department of Mathematics, Faculty of Science, Naresaun University, Phitsanulok 65000, Thailand
Worachead Sommanee: Department of Mathematics and Statistics, Faculty of Science and Technology, Chiang Mai Rajabhat University, Chiang Mai 50300, Thailand

Mathematics, 2023, vol. 11, issue 10, 1-12

Abstract: For a nonempty set X , let T ( X ) be the total transformation semigroup on X . In this paper, we consider the subsemigroups of T ( X ) which are defined by T ( X , Y ) = { α ∈ T ( X ) : X α ⊆ Y } and S ( X , Y ) = { α ∈ T ( X ) : Y α ⊆ Y } where Y is a non-empty subset of X . We characterize the left regular and right regular elements of both T ( X , Y ) and S ( X , Y ) . Moreover, necessary and sufficient conditions for T ( X , Y ) and S ( X , Y ) to be left regular and right regular are given. These results are then applied to determine the numbers of left and right regular elements in T ( X , Y ) for a finite set X .

Keywords: regular elements; magnifying elements; transformation semigroups (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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