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Journals / Turkish Journal of Mathematics / 2014 / Cilt: 38 - Sayı: 3

On transformations of index 1

Leyla BUGAY
Osman KELEKCİ
Pages
419–425
Publication Date
2014-05-16
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

The aim of this paper is to find some properties of the elements of index 1 in Tn, which we call transformations of index 1.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:The index and the period of an element a of a finite semigroup are defined as the smallest values of m \geq 1 and r \geq 1 such that am+r=am, respectively.
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Key Findings & Data:If m=1 then a is called an element of index 1.
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Conclusion & Impact:The aim of this paper is to find some properties of the elements of index 1 in Tn, which we call transformations of index 1.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Transformations · orbit · index

Abstract

The index and the period of an element a of a finite semigroup are defined as the smallest values of m \geq 1 and r \geq 1 such that am+r=am, respectively. If m=1 then a is called an element of index 1. The aim of this paper is to find some properties of the elements of index 1 in Tn, which we call transformations of index 1.

Özet

The index and the period of an element a of a finite semigroup are defined as the smallest values of m \geq 1 and r \geq 1 such that am+r=am, respectively. If m=1 then a is called an element of index 1. The aim of this paper is to find some properties of the elements of index 1 in Tn, which we call transformations of index 1.

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Cite This Article

BUGAY, L., KELEKCİ, O. (2014). On transformations of index 1. Turkish Journal of Mathematics, Cilt: 38 - Sayı: 3, 419–425. https://ajindex.com/articles/185672

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References (2)

  1. Ayık G, Ayık H, ¨ Unl¨ u Y, Howie JM. The structure of elements in finite full transformation semigroups. Bull Austral Math Soc 2005; 71: 69–74.
  2. Ganyushkin O, Mazorchuk V. Classical Finite Transformation Semigroups. London, UK: Springer, 2009. Higgins PM. Combinatorial results for semigroups of order-preserving mappings. Math Proc Camb Phil Soc 1993; 113: 281–296. Howie JM. Fundamentals of Semigroup Theory. New York, NY, USA: Oxford University Press, 1995.