Author:
Manuell Graham,Martins-Ferreira Nelson
Abstract
AbstractWeakly 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 $$\theta $$
θ
). These generalise weakly Schreier extensions of monoids, as well as general extensions of semi-abelian varieties (using the $$\theta $$
θ
appearing in their syntactic characterisation). Restricting again to the case of monoids, a different choice of $$\theta $$
θ
leads to a new class of monoid extensions, more general than the weakly Schreier split extensions.
Publisher
Springer Science and Business Media LLC
Subject
Algebra and Number Theory
Reference19 articles.
1. Bourn, D.: Partial Mal’tsevness and partial protomodularity. arXiv:1507.02886v1 (2015)
2. Bourn, D., Janelidze, G.: Protomodularity, descent, and semidirect products. Theory Appl. Categ. 4(2), 37–46 (1998)
3. Bourn, D., Janelidze, G.: Characterization of protomodular varieties of universal algebras. Theory Appl. Categ. 11(6), 143–447 (2003)
4. Bourn, D., Martins-Ferreira, N., Montoli, A., Sobral, M.: Schreier split epimorphisms between monoids. Semigroup Forum 88(3), 739–752 (2014)
5. Bourn, D., Martins-Ferreira, N., Montoli, A., Sobral, M.: Monoids and pointed $$S$$-protomodular categories. Homol. Homotopy Appl. 18(1), 151–172 (2016)