On transformations of index 1
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.
Anahtar Kelimeler:
Transformations, orbit, index, period
On transformations of index 1
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.
Keywords:
Transformations, orbit, index, period,
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- 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.
- 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.
- ISSN: 1300-0098
- Yayın Aralığı: Yılda 6 Sayı
- Yayıncı: TÜBİTAK
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