Aspects of the category SKB of skew braces
Dominique Bourn, Alberto Facchini, Mara Pompili
Abstract
We examine the pointed protomodular category SKB of left skew braces. We study the notion of commutator of ideals in a left skew brace. Notice that in the literature, “product” of ideals of skew braces is often considered. We show that the so-called (Huq = Smith) condition holds for left skew braces. Finally, we give a set of generators for the commutator of two ideals, and prove that every ideal of a left skew brace has a centralizer.
Topics & Concepts
SkewMathematicsBraceCommutatorIdeal (ethics)NoticePure mathematicsProduct (mathematics)Centralizer and normalizerAlgebra over a fieldStructural engineeringComputer scienceGeometryEngineeringLawLie conformal algebraPolitical scienceTelecommunicationsAlgebraic structures and combinatorial modelsRings, Modules, and AlgebrasHomotopy and Cohomology in Algebraic Topology