TY - JOUR

T1 - On orientation-preserving transformations of a chain

AU - Fernandes, Vítor Hugo

AU - Jesus, Manuel Messias

AU - Singha, Boorapa

N1 - info:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UIDB%2F00297%2F2020/PT#

PY - 2021/1/8

Y1 - 2021/1/8

N2 - In this paper, we introduce the notion of an orientation-preserving transformation on an arbitrary chain, as a natural extension for infinite chains of the well known concept for finite chains introduced in 1998 by McAlister and, independently, in 1999 by Catarino and Higgins. We consider the monoid (Formula presented.) of all orientation-preserving partial transformations on a finite or infinite chain X and its submonoids and (Formula presented.) of all orientation-preserving full transformations and of all orientation-preserving partial permutations on X, respectively. The monoid (Formula presented.) of all order-preserving partial transformations on X and its injective counterpart (Formula presented.) are also considered. We study the regularity and give descriptions of the Green’s relations of the monoids (Formula presented.) and (Formula presented.).

AB - In this paper, we introduce the notion of an orientation-preserving transformation on an arbitrary chain, as a natural extension for infinite chains of the well known concept for finite chains introduced in 1998 by McAlister and, independently, in 1999 by Catarino and Higgins. We consider the monoid (Formula presented.) of all orientation-preserving partial transformations on a finite or infinite chain X and its submonoids and (Formula presented.) of all orientation-preserving full transformations and of all orientation-preserving partial permutations on X, respectively. The monoid (Formula presented.) of all order-preserving partial transformations on X and its injective counterpart (Formula presented.) are also considered. We study the regularity and give descriptions of the Green’s relations of the monoids (Formula presented.) and (Formula presented.).

KW - Order-preserving

KW - orientation-preserving

KW - transformation semigroups

UR - http://www.scopus.com/inward/record.url?scp=85099750349&partnerID=8YFLogxK

U2 - 10.1080/00927872.2020.1870996

DO - 10.1080/00927872.2020.1870996

M3 - Article

AN - SCOPUS:85099750349

VL - 49

SP - 2300

EP - 2325

JO - Communications in Algebra

JF - Communications in Algebra

SN - 0092-7872

IS - 6

ER -