Oka family

An Oka family of ideals is a family

G

such that

I + (a) \in G

and

(I : a) \in G

imply

I \in G

.

Table of contents
- Prime ideal principle for an Oka family Oka family

Prime ideal principle for an Oka family

Every ideal maximal outside an Oka family is prime. If

x y \in I

while

x, y \in / I

, both

I + (x)

and

(I : x)

properly contain

I

, contradicting the Oka condition.

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