Năstăsescu, C.; Van Oystaeyen, Fred; Zhou, Borong Smash products for \(G\)-sets, Clifford theory and duality theorems. (English) Zbl 0836.16029 Bull. Belg. Math. Soc. - Simon Stevin 2, No. 4, 389-398 (1995). Motivated by the study of Clifford theory and duality theorems, the authors develop the theory of smash products for \(G\)-sets, where \(G\) is a group. They extend E. Dade’s graded Clifford theory [J. Reine Angew. Math. 369, 40-86 (1986; Zbl 0583.16001)] to the case of \(G\)-set gradations and they also obtain a duality theorem which extends a result of M. Beattie [J. Algebra 115, 303-312 (1988; Zbl 0647.16010)]. Reviewer: J.L.Gómez-Pardo (Santiago de Compostela) MSC: 16W50 Graded rings and modules (associative rings and algebras) 16S40 Smash products of general Hopf actions 16D90 Module categories in associative algebras 16W20 Automorphisms and endomorphisms Keywords:duality theorems; smash products for \(G\)-sets; graded Clifford theory; \(G\)-set gradations Citations:Zbl 0583.16001; Zbl 0647.16010 PDFBibTeX XMLCite \textit{C. Năstăsescu} et al., Bull. Belg. Math. Soc. - Simon Stevin 2, No. 4, 389--398 (1995; Zbl 0836.16029) Full Text: EuDML