Certain ranks of some ideals in symmetric inverse semigroups contains S_n or A_n

Leyla Bugay

Öz


Let I_n, S_n and A_n be the symmetric inverse semigroup, the symmetric group and the alternating group on X_n={1,…,n}, for n≥2, respectively. Also let I_(n,r) be the subsemigroup consists of all partial injective maps with height less than or equal to r for 1≤r≤n-1, and let SI_(n,r)=I_(n,r)∪S_n and AI_(n,r)=I_(n,r)∪A_n. A non-idempotent element whose square is an idempotent is called a quasi-idempotent. In this paper we obtain the rank and the quasi-idempotent rank of SI_(n,r) (of AI_(n,r)). Also we obtain the relative rank and the relative quasi-idempotent rank of SI_(n,r) modulo S_n  (of AI_(n,r) modulo A_n). 


Tam Metin:

PDF

Referanslar


Ayık, G., Ayık, H., Howie, J. M., On factorisations and generators in transformation semigroup, Semigroup Forum, 70, 225–237, (2005).

Ayık, G., Ayık, H., Howie, J. M., Ünlü, Y., Rank properties of the semigroup of singular transformations on a finite set, Communications in Algebra, 36, 2581–2587, (2008).

Bugay L. Quasi-idempotent ranks of some permutation groups and transformation semigroups, Turkish Journal of Mathematics 43, 2390–2395, (2019).

Ganyushkin, O., Mazorchuk, V., Classical Finite Transformation Semigroups, London, Springer-Verlag, (2009).

Garba, G.U., On the idempotent ranks of certain semigroups of order-preserving transformations, Portugaliae Mathematica, 51, 185–204, (1994).

Garba, G. U., Imam, A. T., Products of quasi-idempotents in finite symmetric inverse semigroups, Semigroup Forum, 92, 645–658, (2016).

Howie, J. M., Fundamentals of Semigroup Theory. New York, Oxford University Press, (1995).

Levi, I., McFadden, R. B., S_n-Normal semigroups, Proceedings of the Edinburgh Mathematical Society, 37, 471–476, (1994).

Yiğit, E., Ayık, G., Ayık, H., Minimal relative generating sets of some partial transformation semigroups, Communications in Algebra, 45, 1239–1245, (2017).

Zhao, P., Fernandes, V. H., The ranks of ideals in various transformation monoids, Communications in Algebra, 43, 674-692, (2015).


Refback'ler

  • Şu halde refbacks yoktur.


Telif Hakkı (c) 2020 Leyla Bugay

Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.