On the idempotents of semigroup of partial contractions of a finite chain

Muhammad Mansur ZUBAİRU; Bashir ALİ

doi:https://doi.org/10.47495/okufbed.799385

Makale detayları

On the idempotents of semigroup of partial contractions of a finite chain

Yazarlar:

Muhammad Mansur ZUBAİRU | Bashir ALİ

Yayıncı:

Osmaniye Korkut Ata Üniversitesi

Ana Başlıklar:

Matematik

Dergi:

Osmaniye Korkut Ata University Journal of the Institute of Science and Technology 2021 Vol.4 Issue 3, pp.242-249

Belge Tipi:

Makale

Yayın Tarihi:

12/2021

Belge Dili:

İngilizce

Document ID (Org No.):

2000557034

Sıklık:

Üç Yıllık

pISSN:

2687-3729

DOI:

https://doi.org/10.47495/okufbed.799385

Özet:

 

Let [n]={1,2,…,n}[n]={1,2,…,n}[n]=\{1,2,\ldots,n\} be a finite chain. Let  PnPn\mathcal{P}_{n} and TnTn\mathcal{T}_{n} be Semigroups of partial  and  full transformations on [n][n][n] respectively.  Let CPn={α∈Pn:|xα−yα|≤|x−y|  ∀x,y∈\dom α}CPn={α∈Pn:|xα−yα|≤|x−y|  ∀x,y∈\dom α}\mathcal{CP}_{n}=\{\alpha\in \mathcal{P}_{n}: |x\alpha-y\alpha|\leq|x-y| \ \  \forall x, y\in \dom~\alpha\} and CTn={α∈Tn:|xα−yα|≤|x−y|  ∀x,y∈[n]}CTn={α∈Tn:|xα−yα|≤|x−y|  ∀x,y∈[n]}\mathcal{CT}_{n}=\{\alpha\in \mathcal{T}_{n}: |x\alpha-y\alpha|\leq|x-y| \ \ \forall x, y\in [n]\}, then CPnCPn\mathcal{CP}_{n} and CTnCTn\mathcal{CT}_{n} are  subsemigroups of PnPn\mathcal{P}_{n} and TnTn\mathcal{T}_{n} respectively. In this paper, we characterize the idempotent elements and computed the number of idempotents of height, n−1n−1n-1 and n−2n−2n-2  for the semigroups CPnCPn\mathcal{CP}_{n} and CTnCTn\mathcal{CT}_{n} respectively.

 

Let [n]={1,2,…,n}[n]={1,2,…,n}[n]=\{1,2,\ldots,n\} be a finite chain. Let  PnPn\mathcal{P}_{n} and TnTn\mathcal{T}_{n} be Semigroups of partial  and  full transformations on [n][n][n] respectively.  Let CPn={α∈Pn:|xα−yα|≤|x−y|  ∀x,y∈\dom α}CPn={α∈Pn:|xα−yα|≤|x−y|  ∀x,y∈\dom α}\mathcal{CP}_{n}=\{\alpha\in \mathcal{P}_{n}: |x\alpha-y\alpha|\leq|x-y| \ \  \forall x, y\in \dom~\alpha\} and CTn={α∈Tn:|xα−yα|≤|x−y|  ∀x,y∈[n]}CTn={α∈Tn:|xα−yα|≤|x−y|  ∀x,y∈[n]}\mathcal{CT}_{n}=\{\alpha\in \mathcal{T}_{n}: |x\alpha-y\alpha|\leq|x-y| \ \ \forall x, y\in [n]\}, then CPnCPn\mathcal{CP}_{n} and CTnCTn\mathcal{CT}_{n} are  subsemigroups of PnPn\mathcal{P}_{n} and TnTn\mathcal{T}_{n} respectively. In this paper, we characterize the idempotent elements and computed the number of idempotents of height, n−1n−1n-1 and n−2n−2n-2  for the semigroups CPnCPn\mathcal{CP}_{n} and CTnCTn\mathcal{CT}_{n} respectively.

Makale detayları

On the idempotents of semigroup of partial contractions of a finite chain

Yazarlar: Muhammad Mansur ZUBAİRU | Bashir ALİ

Yayıncı: Osmaniye Korkut Ata Üniversitesi

Ana Başlıklar: Matematik

Dergi: Osmaniye Korkut Ata University Journal of the Institute of Science and Technology 2021 Vol.4 Issue 3, pp.242-249

Belge Tipi: Makale

Yayın Tarihi: 12/2021

Belge Dili: İngilizce

Document ID (Org No.): 2000557034

Sıklık: Üç Yıllık

pISSN: 2687-3729

DOI: https://doi.org/10.47495/okufbed.799385

Sayı

Yazarlar:

Muhammad Mansur ZUBAİRU | Bashir ALİ

Yayıncı:

Osmaniye Korkut Ata Üniversitesi

Ana Başlıklar:

Matematik

Dergi:

Osmaniye Korkut Ata University Journal of the Institute of Science and Technology 2021 Vol.4 Issue 3, pp.242-249

Belge Tipi:

Makale

Yayın Tarihi:

12/2021

Belge Dili:

İngilizce

Document ID (Org No.):

2000557034

Sıklık:

Üç Yıllık

pISSN:

2687-3729

DOI:

https://doi.org/10.47495/okufbed.799385