Control subgroups and birational extensions of graded rings

Salah El Din S. Hussein

International Journal of Mathematics and Mathematical Sciences, 1999, vol. 22, 1-5

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.

Date: 1999
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:491950

DOI: 10.1155/S0161171299224118

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