2020/12/13 by Sebastian Cristian Lesnic, Lesnic, Sebastian Cristian
Mathematics · #08A05 #18B99 (Secondary) #20N99 (Primary) #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2012.07052
openalex publication_date 2020/12/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The article - part of a larger thesis which aims to give a detailed\ndescription of the generalisation to the category of groups with operators of\nthe classical theory of semisimplicity for modules - presents a\nstraightforward generalisation to groups with operators of a number of\ninvariants well-known in the theory of modules, having a special bearing on\nphenomena of semisimplicity. The behaviour of these generalised invariants in\nrelation to the fundamental construction of restricted direct sums and in\nparticular in the context of semisimple groups with operators is in particular\nexamined. The article also introduces a particular type of morphisms between\ngroups with operators, morphisms which naturally preserve the generalised\ninvariants in question and thus show themselves to be an adequate notion for\nthe study of semisimplicity in the more general frame considered.\n