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On Mackey decomposition theorems and Maschke’s theorem for strongly group-graded rings. (Chinese. English summary) Zbl 0762.16017

Summary: Let \(A=\bigoplus_{g\in G} A_ g\) be a strongly graded ring by a multiplicative group \(G\). Two Mackey decomposition theorems and a generalization of Maschke’s theorem are given, also the relation of the Jacobson radicals of \(A\) and \(A_ 1\) which is the 1-component of \(A\) is studied, where 1 is the identity of \(G\).

MSC:

16W50 Graded rings and modules (associative rings and algebras)
16N20 Jacobson radical, quasimultiplication
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