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

Leyla BUGAY

doi:https://doi.org/10.25092/baunfbed.745821

Article Details

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

Authors:

Leyla BUGAY

Publisher:

Balıkesir University

Main Topics:

Astronomy and allied sciences

Journal:

Journal of Balıkesir University Institute of Science and Technology 2020 Vol.22 Issue 2, pp.669-678

Document Type:

Article

Publication Date:

4/2020

Document Language:

English

Document ID (Org No.):

2000925014

Frequency:

Bi-Annual

eISSN:

2536-5142

pISSN:

1301-7985

DOI:

https://doi.org/10.25092/baunfbed.745821

Keywords:

Abstract:

 

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).

 

n≥2 için I_n, S_n ve A_n, sırasıyla, X_n={1,…,n} üzerindeki simetrik inverse yarıgrup, simetrik grup ve alterne grup olsun. Ayrıca, 1≤r≤n-1 için I_(n,r), yüksekliği en fazla r olan tüm kısmi bire-bir dönüşümlerden oluşan altyarıgrup, SI_(n,r)=I_(n,r)∪S_n ve AI_(n,r)=I_(n,r)∪A_n olsun. Karesi idempotent olan fakat kendisi idempotent olmayan bir elemana quasi-idempotent denir. Bu calışmada SI_(n,r) (AI_(n,r)) nin rankını elde ettik. Ayrıca, modulo S_n e göre SI_(n,r) nin (modulo A_n e göre AI_(n,r) nin) ilişkili rankını ve quasi-ilişkili rankını elde ettik.

Article Details

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

Authors:

Leyla BUGAY

Publisher:

Balıkesir University

Main Topics:

Astronomy and allied sciences

Journal:

Journal of Balıkesir University Institute of Science and Technology 2020 Vol.22 Issue 2, pp.669-678

Document Type:

Article

Publication Date:

4/2020

Document Language:

English

Document ID (Org No.):

2000925014

Frequency:

Bi-Annual

eISSN:

2536-5142

pISSN:

1301-7985

DOI:

https://doi.org/10.25092/baunfbed.745821

Simetrik inverse yarıgrup

quasi-idempotent

rank

Issues

Article Details

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

Authors: Leyla BUGAY

Publisher: Balıkesir University

Main Topics: Astronomy and allied sciences

Journal: Journal of Balıkesir University Institute of Science and Technology 2020 Vol.22 Issue 2, pp.669-678

Document Type: Article

Publication Date: 4/2020

Document Language: English

Document ID (Org No.): 2000925014

Frequency: Bi-Annual

eISSN: 2536-5142

pISSN: 1301-7985

DOI: https://doi.org/10.25092/baunfbed.745821

Simetrik inverse yarıgrup

quasi-idempotent

rank

Issues

Authors:

Leyla BUGAY

Publisher:

Balıkesir University

Main Topics:

Astronomy and allied sciences

Journal:

Journal of Balıkesir University Institute of Science and Technology 2020 Vol.22 Issue 2, pp.669-678

Document Type:

Article

Publication Date:

4/2020

Document Language:

English

Document ID (Org No.):

2000925014

Frequency:

Bi-Annual

eISSN:

2536-5142

pISSN:

1301-7985

DOI:

https://doi.org/10.25092/baunfbed.745821