International Journal of Mathematics and Mathematical Sciences

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International Journal of Mathematics and Mathematical Sciences / 1999 / Article

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Volume 22 |Article ID 491950 | 5 pages | https://doi.org/10.1155/S0161171299224118

Control subgroups and birational extensions of graded rings

Salah El Din S. Hussein1

1Department of Mathematics, Faculty of Science, Ain Shams University, Abbassia, Cairo 11566, Egypt

Received17 Apr 1998

Abstract

In this paper, we establish the relation between the concept of control subgroups and the class of graded birational algebras. Actually, we prove that if R=⊕σ∈GRσ is a strongly G-graded ring and H⊲G, then the embedding i:R(H)↪R, where R(H)=⊕σ∈HRσ, is a Zariski extension if and only if H controls the filter ℒ(R−P) for every prime ideal P in an open set of the Zariski topology on R. This enables us to relate certain ideals of R and R(H) up to radical.

Copyright © 1999 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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