Minimale Erzeugendensystem und minimale Primteiler von monomialen Radikalidealen.
Ring extensions with some finiteness conditions on the set of intermediate rings
A ring extension is said to be FO if it has only finitely many intermediate rings. 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 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...
Equations for the set of overrings of normal rings and related ring extensions
We establish several finiteness characterizations and equations for the cardinality and the length of the set of overrings of rings with nontrivial zero divisors and integrally closed in their total ring of fractions. Similar properties are also obtained for related extensions of commutative rings that are not necessarily integral domains. Numerical characterizations are obtained for rings with some finiteness conditions afterwards.
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