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Control subgroups and birational extensions of graded rings

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  • Salah El Din S. Hussein

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 ∈ G R σ is a strongly G -graded ring and H ⊲ G , then the embedding i : R ( H ) ↪ R , where R ( H ) = ⊕ σ ∈ H R σ , 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.

Suggested Citation

  • Salah El Din S. Hussein, 1999. "Control subgroups and birational extensions of graded rings," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 22, pages 1-5, January.
    • Handle: RePEc:hin:jijmms:491950
    DOI: 10.1155/S0161171299224118
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