Weakly Schreier extensions for general algebras. (English) Zbl 1539.18012
Summary: 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 syntactic 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.
MSC:
| 18G50 | Nonabelian homological algebra (category-theoretic aspects) |
| 08C05 | Categories of algebras |
| 20M50 | Connections of semigroups with homological algebra and category theory |
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