Group graded rings and smash products
Let \(G\) be a finite group with identity element \(e\). Let \(R\) be a \(G\)-graded algebra over a commutative ring \(k\). As in a paper by \textit{M. Cohen} and \textit{S. Montgomery} [Trans. Am. Math. Soc. 282, 237--258 (1984; Zbl 0533.16001)], one forms the smash product \(R\#(kG)^*\) (where \((kG)^*\) is the dual of the group ring \(kG)\), and deduces from certain duality theorems, various connections between \(R\), \(R_e\) and \(R\#(kG)^*\). In this paper the authors characterize \(R\#(kG)^*\) via endomorphism rings of an \(R\)-generator. They deduce from it a slight generalization of the duality theorems proved by Cohen and Montgomery.
scientific article; zbMATH DE number 3970958