On the maximal regular subsemigroups of ideals of order-preserving or order-reversing transformations

The Regular Part of a Semigroup of Full Transformations with Restricted Range: Maximal Inverse Subsemigroups and Maximal Regular Subsemigroups of Its Ideals

“…Let be a chain and OT( ) the full order-preserving transformation semigroup on . In 2011, Dimitrova and Koppitz [22] characterized the maximal regular subsemigroups of ideals of OT( ) when is a finite chain. In 2015, Sommanee and Sanwong [23] investigated the regularity and Green's relations of the order-preserving transformation semigroup…”

On certain semigroups of full contraction maps of a finite chain

“…In [8], a description of the endomorphisms of O n was presented. Other algebraic properties in the semigroup O n and some of its notable subsemigroups and oversemigroups may be found in [3][4][5][6][7]9 [16][17][18][19][20][21]. In this current article we consider an algebra study for the so-called subsemigroups of contraction mappings of T n .…”

“…In [8], a description of the endomorphisms of O n was presented. Other algebraic properties in the semigroup O n and some of its notable subsemigroups and oversemigroups may be found in [3][4][5][6][7]9]. On a semigroup S the relation L * is defined by the rule that (a, b) ∈ L * if and only if a, b are related by the Green's relation L in some over semigroup of S .…”

Regular semigroups of partial transformations preserving a fence N

“…In [14], regular elements of some order-preserving transformation semigroups are investigated. A characterization of the maximal regular subsemigroups of ideals of order-preserving or order-reversing transformations was given in [4]. Note that the semigroup OP N of all partial transformations preserving the fence N is not regular.…”

“…After that many authors studied maximal regular subsemigroups of transformations preserving an order (e.g. [4,17,18]). The purpose of this paper is to study (maximal) regular subsemigroups of OP N .…”