Hussein, Salah El Din S. Control subgroups and birational extensions of graded rings. (English) Zbl 0932.16042 Int. J. Math. Math. Sci. 22, No. 2, 411-415 (1999). Let \(R\) be a strongly \(G\)-graded ring and \(H\) a normal subgroup of \(G\). The author proves that \(R^{(H)}\subseteq R\) is a Zariski extension if and only if the filter \({\mathcal L}(R-P)\) is controlled by \(H\) for any prime ideal \(P\) in an open set of the Zariski topology on \(R\). As an application certain ideals of \(R\) and \(R^{(H)}\) are related up to radical. Reviewer: C.Năstăsescu (Bucureşti) MSC: 16W50 Graded rings and modules (associative rings and algebras) 16S34 Group rings 16S90 Torsion theories; radicals on module categories (associative algebraic aspects) 16D25 Ideals in associative algebras Keywords:control subgroups; birational extensions; Zariski extensions; Gabriel filters; kernel functors; strongly graded rings PDFBibTeX XMLCite \textit{S. E. D. S. Hussein}, Int. J. Math. Math. Sci. 22, No. 2, 411--415 (1999; Zbl 0932.16042) Full Text: DOI EuDML