2022/12/14 by Maria Manuel Clementino, Clementino, Maria Manuel, Carla Ruivo +1
Computer Science · Decision Sciences · Mathematics · #06F15 #08C05 #18E13 #Advanced Algebra and Logic #Category Theory (math.CT) #FOS: Mathematics #Fuzzy and Soft Set Theory #Group Theory (math.GR) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2212.07064
openalex publication_date 2022/12/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We investigate the behaviour of split extensions in the category OrdGrp of (pre)\-ordered groups. Namely we show that the lexicographic order plays a key role on the existence of compatible orders for semidirect products, establishing necessary and sufficient conditions for such existence; we prove that the Split Short Five Lemma holds for stably strong split extensions, and identify classes of split extensions which admit a classifier.