Characterization of quasi idempotent in semigroups of full contraction mappings
Keywords:
Semigroup, Contraction mapping, Quasi-idempotentAbstract
Let Tn be the semigroup of full transformation of a finite set and let Xn = {1, 2, · · · , n}. A transformation α : Domα ⊂ Xn →Im(α) ⊂ Xn is said to be full or total transformation if Domα = Xn. A transformation β ∈ CT n is said to be full contraction mapping if ∀ x, y ∈ Domα, |xα − yα| ≤ |x − y| ∀ x, y ∈ Domα. Let CT n be the semigroup of full contraction transformation and let QCT n be its quasi-idempotent of full contraction transformation of Xn. In this paper, we characterized quasi-idempotent elements into matching blocks, non-matching blocks and self matching blocks of CT n and later come up with a strong and useful theorem
References
A. D. Adeshola & A. Umar, ‘‘Combinatorial results for certain semigroups of order preserving full contraction mappings of a finite chain’’, J combin. Math. Combin. comput 106 (2018) 37. https://squ.elsevierpure.com/en/publications/combinatorial-results-for-certain-semigroups-of-order-preserving-.
A. T. Imam, S. Ibrahim, G. U. Garba, L. Usman & A. Idris, ‘‘Quasi-idempotents in finite semigroup of full order-preserving transformations’’, Algebra and Discrete Mathematics 35 (2023) 62. https://doi.org/10.12958/adm1846.
G. U. Garba, A. T. Imam & B. A. Madu, ‘‘Products of quasi-idempotentm in finite symmetric inverse semi-groups’’, Semi-group forum 92 (2016) 645. https://www.academia.edu/80610112/Products_of_quasi_idempotents_in_finite_symmetric_inverse_semigroups.
G. U. Garba, A. T. Imam & B. A. Madu, ‘‘On Certain Semi-groups of full contraction maps of a finite chain’’, Turkish J. Math. 41 (2017) 500. https://doi.org/10.3906/mat-1602-52.
J. M. Howie Fundamentals of semigroup theory, Clarendon Press, Oxford, 1995. https://global.oup.com/academic/product/fundamentals-of-semigroup-theory-9780198511946?cc=us&lang=en&.
G. R. Ibrahim, A. T. Imam, A. D. Adeshola & G. N. Bakare, ‘‘Some Algebraic Properties of Order-Preserving Full Contraction Transformation Semigroup’’, Journal of Semigroup Theory 2019 (2019) 2. https://scik.org/index.php/jsta/article/view/3931.
N. J. A. Sloane (Ed.), The On-Line Encyclopedia of Integer Sequences, 2011. Available at https://oeis.org/.
Published
How to Cite
Issue
Section
Copyright (c) 2024 A. D. Adeshola, S. O. Akande, R. G. Ibrahim, J. O. Lawal (Author)
This work is licensed under a Creative Commons Attribution 4.0 International License.
