Krullring

A Krullring (after Wolfgang Krull ) is an integrity domain with the following property: ${\displaystyle A}$

There is a set whose elements are discrete evaluation rings of the quotient field such that the following two conditions are met: ${\displaystyle M}$ ${\displaystyle K:={\text{Quot}}(A)}$

• ${\displaystyle A=\bigcap _{R\in M}R}$
• For each out , there are only a finite number of evaluation rings , whose respective maximum ideal is contained. (Evaluation rings are local rings , i.e. they each have only one maximum ideal) ${\displaystyle x\neq 0}$ ${\displaystyle A}$ ${\displaystyle M}$ ${\displaystyle x}$

The first condition means: the average of the rating rings is off . ${\displaystyle A}$ ${\displaystyle M}$