2023/11/07 by Alberto Facchini, Facchini, Alberto, David Stanovský +1 · 1 citation
Mathematics · #08B25 #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Rings and Algebras (math.RA) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2311.04321
openalex publication_date 2023/11/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
First of all, we recall the well known notion of semidirect product both for classical algebraic structures (like groups and rings) and for more recent ones (digroups, left skew braces, heaps, trusses). Then we analyse the concept of semidirect product for an arbitrary algebra A in a variety \calV of type~\calF. An inner semidirect-product decomposition A=B \ltimesω of A consists of a subalgebra B of A and a congruence ω on A such that B is a set of representatives of the congruence classes of A modulo ω. An outer semidirect product is the restriction to B of a functor from a suitable category \calCB containing B, called the enveloping category of B, to the category Set_* of pointed sets.