TY  - JOUR
T1  - On the idempotents of semigroup of partial contractions of a finite chain
TT  - On the idempotents of semigroup of partial contractions of a finite chain
AU  - Zubairu, Muhammad Mansur
AU  - Ali, Bashir
PY  - 2021
DA  - December
Y2  - 2021
DO  - 10.47495/okufbed.799385
JF  - Osmaniye Korkut Ata Üniversitesi Fen Bilimleri Enstitüsü Dergisi
JO  - Osmaniye Korkut Ata University Journal of The Institute of Science and Techno
PB  - Osmaniye Korkut Ata Üniversitesi
WT  - DergiPark
SN  - 2687-3729
SP  - 242
EP  - 249
VL  - 4
IS  - 3
LA  - en
AB  - Let $[n]=\{1,2,\ldots,n\}$ be a finite chain. Let  $\mathcal{P}_{n}$ and $\mathcal{T}_{n}$ be Semigroups of partial  and  full transformations on $[n]$ respectively.  Let $\mathcal{CP}_{n}=\{\alpha\in \mathcal{P}_{n}: |x\alpha-y\alpha|\leq|x-y| \ \  \forall x, y\in \dom~\alpha\}$ and $\mathcal{CT}_{n}=\{\alpha\in \mathcal{T}_{n}: |x\alpha-y\alpha|\leq|x-y| \ \ \forall x, y\in [n]\}$, then $\mathcal{CP}_{n}$ and $\mathcal{CT}_{n}$ are  subsemigroups of $\mathcal{P}_{n}$ and $\mathcal{T}_{n}$ respectively. In this paper, we characterize the idempotent elements and computed the number of idempotents of height, $n-1$ and $n-2$  for the semigroups $\mathcal{CP}_{n}$ and $\mathcal{CT}_{n}$ respectively.
KW  - Transformations semigroup
KW  - Contractions maps
KW  - idempotents
N2  - Let $[n]=\{1,2,\ldots,n\}$ be a finite chain. Let  $\mathcal{P}_{n}$ and $\mathcal{T}_{n}$ be Semigroups of partial  and  full transformations on $[n]$ respectively.  Let $\mathcal{CP}_{n}=\{\alpha\in \mathcal{P}_{n}: |x\alpha-y\alpha|\leq|x-y| \ \  \forall x, y\in \dom~\alpha\}$ and $\mathcal{CT}_{n}=\{\alpha\in \mathcal{T}_{n}: |x\alpha-y\alpha|\leq|x-y| \ \ \forall x, y\in [n]\}$, then $\mathcal{CP}_{n}$ and $\mathcal{CT}_{n}$ are  subsemigroups of $\mathcal{P}_{n}$ and $\mathcal{T}_{n}$ respectively. In this paper, we characterize the idempotent elements and computed the number of idempotents of height, $n-1$ and $n-2$  for the semigroups $\mathcal{CP}_{n}$ and $\mathcal{CT}_{n}$ respectively.
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UR  - https://doi.org/10.47495/okufbed.799385
L1  - https://dergipark.org.tr/tr/download/article-file/1307229
ER  -