Abstract:
In this article we present 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. We examine the behaviour of the generalised invariants in relation to the fundamental construction of restricted direct sums and in particular in the context of semisimple groups with operators. We also consider a particular type of morphisms between groups with operators, which naturally preserves the generalised invariants in question and thus shows itself to be an adequate notion for their study in the more general frame considered.
Key Words: Groups of operators, theory of modules.
2010 Mathematics Subject Classification: Primary 20N99; Secondary 08A05, 08A35.
