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Ring extensions with some finiteness conditions on the set of intermediate rings

Ali Jaballah (2010)

Czechoslovak Mathematical Journal

A ring extension R S is said to be FO if it has only finitely many intermediate rings. R S is said to be FC if each chain of distinct intermediate rings in this extension is finite. We establish several necessary and sufficient conditions for the ring extension R S to be FO or FC together with several other finiteness conditions on the set of intermediate rings. As a corollary we show that each integrally closed ring extension with finite length chains of intermediate rings is necessarily a normal pair...

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