Classifying Finitely Generated Indecomposable RA Loops

TL;DR

This paper extends the classification of finite ring alternative loops to all finitely generated RA loops, providing a comprehensive explicit description of these algebraic structures.

Contribution

It generalizes previous classification results from finite to finitely generated RA loops, offering a detailed explicit description.

Findings

Extended classification to finitely generated RA loops.

Provided explicit descriptions of all such loops.

Generalized prior finite case results.

Abstract

In 1995, E. Jespers, G. Leal and C. Polcino Milies classified all finite ring alternative loops (RA loops for short) which are not direct products of proper subloops. In this paper we extend this result to finitely generated RA loops and provide an explicit description of all such loops.