scholarly journals The Relative Rank of Transformation Semigroups with Restricted Range on a Finite Chain

2021 ◽  
Vol 9 (5) ◽  
pp. 718-723
Author(s):  
Kittisak Tinpun
Keyword(s):  
Restricted Range ◽  
Finite Chain ◽  
Transformation Semigroups ◽  
Relative Rank

scholarly journals On relative ranks of finite transformation semigroups with restricted range

2021 ◽  
Vol 73 (5) ◽  
pp. 617-626
Author(s):  
I. Dimitrova ◽  
J. Koppitz
Keyword(s):  
Restricted Range ◽  
Finite Chain ◽  
Transformation Semigroups ◽  
Relative Rank ◽  
Generating Sets ◽  
Finite Transformation

UDC 512.5 We determine the relative rank of the semigroup of all transformations on a finite chain with restricted range modulo the set of all orientation-preserving transformations in Moreover, we state the relative rank of the semigroup modulo the set of all order-preserving transformations in In both cases we characterize the minimal relative generating sets.  

Characterizations of Cayley graphs of finite transformation semigroups with restricted range

2020 ◽  
pp. 2150041
Author(s):  
Chunya Tisklang ◽  
Sayan Panma
Keyword(s):  
Cayley Graphs ◽  
Transformation Semigroup ◽  
Restricted Range ◽  
Transformation Semigroups ◽  
Finite Transformation ◽  
Empty Subset

The transformation semigroup with restricted range [Formula: see text] is the set of all functions from a set [Formula: see text] into a non-empty subset [Formula: see text] of [Formula: see text]. In this paper, we characterize Cayley graphs of [Formula: see text] with the connection set [Formula: see text]. Moreover, the undirected property of Cayley graphs Cay [Formula: see text] is studied.

scholarly journals Regular order-preserving transformation semigroups

2000 ◽  
Vol 62 (3) ◽  
pp. 511-524 ◽  
Author(s):  
Yupaporn Kemprasit ◽  
Thawhat Changphas
Keyword(s):  
Finite Chain ◽  
Transformation Semigroups

The semigroup OT (X) of all order-preserving total transformations of a finite chain X is known to be regular. We extend this result to subchains of Z; and we characterise when OT (X) is regular for an interval X in R. We also consider the corresponding idea for partial transformations of arbitrary chains and posets.

scholarly journals On Divisors of Pseudovarieties Generated by Some Classes of Full Transformation Semigroups

2008 ◽  
Vol 15 (04) ◽  
pp. 581-588
Author(s):  
Vítor H. Fernandes
Keyword(s):  
Finite Chain ◽  
Transformation Semigroups ◽  
Full Transformation ◽  
Division Theorem

In this paper we present a division theorem for the pseudovariety of semigroups 𝖮𝖣 (𝖮𝖱) generated by all semigroups of order-preserving or order-reversing (orientation-preserving or orientation-reversing) full transformations on a finite chain.

scholarly journals Structure of principal one-sided ideals

2021 ◽  
pp. 1-53
Author(s):  
James East
Keyword(s):  
Structural Analysis ◽  
Restricted Range ◽  
Transformation Semigroups ◽  
Inverse Monoids ◽  
Full Transformation

We give a thorough structural analysis of the principal one-sided ideals of arbitrary semigroups, and then apply this to full transformation semigroups and symmetric inverse monoids. One-sided ideals of these semigroups naturally occur as semigroups of transformations with restricted range or kernel.

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