Structure of principal one-sided ideals
James East
TL;DR
This paper provides a detailed structural analysis of principal one-sided ideals in semigroups, with applications to transformation semigroups and inverse monoids, revealing their formation as transformation sets with specific restrictions.
Contribution
It introduces a comprehensive framework for understanding principal one-sided ideals in various semigroups, including full transformation semigroups and symmetric inverse monoids.
Findings
Characterization of principal one-sided ideals in semigroups
Application to transformation semigroups with restricted range or kernel
Structural insights into inverse monoids
Abstract
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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