Control subgroups and birational extensions of graded rings
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 is a strongly -graded ring and , then the embedding , where , is a Zariski extension if and only if controls the filter for every prime ideal in an open set of the Zariski topology on . This enables us to relate certain ideals of and up to radical.
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