Regularity of  semigroups of transformations with restricted range preserving an alternating orientation order

Somphong JITMAN; Rattana SRITHUS; Chalermpong WORAWANNOTAI

Makale detayları

Regularity of semigroups of transformations with restricted range preserving an alternating orientation order

Yazarlar:

Somphong JITMAN | Rattana SRITHUS | Chalermpong WORAWANNOTAI

Yayıncı:

TUBITAK

Dergi:

Turkish Journal of Mathematics 2018 Vol.42 Issue 4, pp.1913-1926

Belge Tipi:

Makale

Yayın Tarihi:

7/2018

Belge Dili:

Türkçe

Document ID (Org No.):

2000745835

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098

Özet:

 

It is well known that the transformation semigroup on a nonempty set XXX, which is denoted by T(X)T(X)T(X), is regular,   but its subsemigroups do not need to be.   Consider a finite ordered set X=(X;≤)X=(X;≤)X=(X;\leq) whose order forms a path with alternating orientation.   For a nonempty subset YYY of XXX, two subsemigroups of T(X)T(X)T(X) are studied. Namely,  the semigroup   OT(X,Y)={α∈T(X)∣α is order-preserving and Xα⊆Y}OT(X,Y)={α∈T(X)∣α is order-preserving and Xα⊆Y}OT(X,Y)=\{\alpha\in T(X)\mid \alpha~\text{is order-preserving and }X\alpha\subseteq Y\}  and the semigroup   OS(X,Y)={α∈T(X)∣αOS(X,Y)={α∈T(X)∣αOS(X,Y)=\{\alpha\in T(X)\mid\alpha is order-preserving and  Yα⊆Y}Yα⊆Y}Y\alpha \subseteq Y\}.  In this paper, we characterize ordered sets having a coregular semigroup OT(X,Y)OT(X,Y)OT(X,Y) and a coregular semigroup OS(X,Y)OS(X,Y)OS(X,Y), respectively.  Some characterizations of regular semigroups OT(X,Y)OT(X,Y)OT(X,Y) and OS(X,Y)OS(X,Y)OS(X,Y) are given.  We also describe coregular and regular elements of both OT(X,Y)OT(X,Y)OT(X,Y) and OS(X,Y)OS(X,Y)OS(X,Y).

Makale detayları

Regularity of semigroups of transformations with restricted range preserving an alternating orientation order

Yazarlar: Somphong JITMAN | Rattana SRITHUS | Chalermpong WORAWANNOTAI

Yayıncı: TUBITAK

Dergi: Turkish Journal of Mathematics 2018 Vol.42 Issue 4, pp.1913-1926

Belge Tipi: Makale

Yayın Tarihi: 7/2018

Belge Dili: Türkçe

Document ID (Org No.): 2000745835

Sıklık: İki Aylık

eISSN: 1303-6149

pISSN: 1300-0098

Sayı

Yazarlar:

Somphong JITMAN | Rattana SRITHUS | Chalermpong WORAWANNOTAI

Yayıncı:

TUBITAK

Dergi:

Turkish Journal of Mathematics 2018 Vol.42 Issue 4, pp.1913-1926

Belge Tipi:

Makale

Yayın Tarihi:

7/2018

Belge Dili:

Türkçe

Document ID (Org No.):

2000745835

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098