Sym\'etrons et K-boucles omega-stables

TL;DR

This paper develops the model theory for omega-stable K-loops and symétrons, extending foundational work by Poizat and adapting Lascar's analysis to this algebraic context.

Contribution

It establishes an appropriate indecomposability theorem and adapts Lascar's analysis for omega-stable K-loops and symétrons, advancing the theoretical understanding.

Findings

Established an indecomposability theorem for omega-stable K-loops and symétrons.

Adapted Lascar's analysis to the context of omega-stable K-loops.

Extended Poizat's foundational work in this area.

Abstract

We develop the model theory of omega-stable K-loops and 'sym\'etrons'. Continuing Poizat's seminal work, we notably establish an appropriate version of the indecomposability theorem and we adapt Lascar's analysis to this context. -- Nous d\'eveloppons la th\'eorie des mod\`eles des K-boucles et des sym\'etrons omega-stables. En poursuivant le travail s\'eminal de Poizat, nous \'etablissons notamment une version appropri\'ee du th\'eor\`eme des ind\'ecomposables et nous adaptons l'analyse de Lascar \`a ce contexte.