The generalisation of some invariants of modules to groups with operators
Abstract
The article part of a larger thesis which aims to give a detailed description of the generalisation to the category of groups with operators of the classical theory of semisimplicity for modules presents a straightforward generalisation to groups with operators of a number of invariants well-known in the theory of modules, having a special bearing on phenomena of semisimplicity. The behaviour of these generalised invariants in relation to the fundamental construction of restricted direct sums and in particular in the context of semisimple groups with operators is in particular examined. The article also introduces a particular type of morphisms between groups with operators, morphisms which naturally preserve the generalised invariants in question and thus show themselves to be an adequate notion for the study of semisimplicity in the more general frame considered.
Cite
@article{arxiv.2012.07052,
title = {The generalisation of some invariants of modules to groups with operators},
author = {Sebastian Cristian Lesnic},
journal= {arXiv preprint arXiv:2012.07052},
year = {2020}
}
Comments
14 pages. Article to be published soon (after the current moment of December 13 2020) in the "Bulletin Math\'ematique de la Soci\'et\'e des Sciences Math\'ematiques de Roumanie"