On the structure of braces whose subideals are ideals

TL;DR

This paper introduces the concept of T-braces, a class of skew left braces with abelian type where the ideal relation is transitive, exploring their structural properties.

Contribution

It initiates the study of T-braces, defining their structure and properties, and analyzing the transitivity of the ideal relation in these algebraic objects.

Findings

T-braces have a transitive ideal relation.

Structural properties of T-braces are characterized.

Foundations for further research on T-braces are established.

Abstract

This article begins the study of T-braces, those skew left braces of abelian type in which the relation of being an ideal is a transitive relation.