Năstăsescu, C.; Rodinò, N. Group graded rings and smash products. (English) Zbl 0602.16002 Rend. Semin. Mat. Univ. Padova 74, 129-137 (1985). 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 M. Cohen and 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. Reviewer: Miriam Cohen (Beer-Sheva) Cited in 3 Documents MSC: 16W50 Graded rings and modules (associative rings and algebras) 16W30 Hopf algebras (associative rings and algebras) (MSC2000) 16W20 Automorphisms and endomorphisms 16S34 Group rings 16D90 Module categories in associative algebras Keywords:G-graded algebra; smash product; dual of the group ring; duality theorems; endomorphism rings Citations:Zbl 0533.16001 PDFBibTeX XMLCite \textit{C. Năstăsescu} and \textit{N. Rodinò}, Rend. Semin. Mat. Univ. Padova 74, 129--137 (1985; Zbl 0602.16002) Full Text: Numdam References: [1] M. Cohen - S. Montgomery , Group-Graded Rings, Smash Product and Group Actions , Trans. Am. Math. Soc. , 282 , no. 1 ( 1984 ), pp. 237 - 258 . MR 728711 | Zbl 0533.16001 · Zbl 0533.16001 · doi:10.2307/1999586 [2] C. N - F. Van Oystaeyen , Graded Ring Theory , North-Holland, Math. Library , Vol. 28 ( 1982 ). MR 676974 | Zbl 0494.16001 · Zbl 0494.16001 [3] Bo Stenström , Rings of Quotients , Springer-Verlag , Berlin , 1975 . MR 389953 | Zbl 0296.16001 · Zbl 0296.16001 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.