2024/03/12 by A. R. Chekhlov, Peter Danchev, Chekhlov, Andrey R. +3
Mathematics · #20K21 #Advanced Topics in Algebra #FOS: Mathematics #Group Theory (math.GR) #Rings and Algebras (math.RA) #Rings, Modules, and Algebras #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.2403.08096
openalex publication_date 2024/03/12 · openalex created_date 2024/03/15 · openalex updated_date 2026/07/28
Trying to finalize in some way the present subject, this paper targets to generalize substantially the notions of Bassian and co-Bassian groups by introducing the so-called finitely (co-)Bassian groups, semi (co-)Bassian groups, fully generalized (co-)Bassian groups, absolutely generalized (co-)Bassian groups and establishing their crucial properties and characterizations. In fact, some of the concepts give nothing new by coinciding in the reduced case with the well-known (co-)Bassian property. However, in some of the definitions, the situation is slightly more complicated and we obtain a few new and interesting things by showing that the extensions of the Bassian and co-Bassian properties are totally distinct each other.