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arXiv · 2211.01132

Weakly Schreier extensions for general algebras

Graham Manuell·Nelson Martins-Ferreira
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Abstract

Weakly Schreier split extensions are a reasonably large, yet well-understood class of monoid extensions, which generalise some aspects of split extensions of groups. This short note provides a way to define and study similar classes of split extensions in general algebraic structures (parameterised by a term $\theta$). These generalise weakly Schreier extensions of monoids, as well as general extensions of semi-abelian varieties (using the $\theta$ appearing in their syntactical characterisation). Restricting again to the case of monoids, a different choice of $\theta$ leads to a new class of monoid extensions, more general than the weakly Schreier split extensions.

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Graham Manuell, Nelson Martins-Ferreira. 2022-11-02. Weakly Schreier extensions for general algebras. https://doi.org/10.1007/s00012-023-00823-7

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