In commutative algebra, the Krull–Akizuki theorem states the following: Let A be a one-dimensional reduced noetherian ring, K its total ring of fractions. Suppose L is a finite extension of K. If A ⊂ B ⊂ L {\displaystyle A\subset B\subset L} and B is reduced, then B is a noetherian ring of dimension at most one.
In commutative algebra, the Krull–Akizuki theorem states the following: Let A be a one-dimensional reduced noetherian ring, K its total ring of fractions. Suppose L is a finite extension of K. If A ⊂ B ⊂ L {\displaystyle A\subset B\subset L} and B is reduced, then B is a noetherian ring of dimension at most one.
Source: Wikipedia "Krull–Akizuki theorem" · CC BY-SA 4.0
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