Arithmetical ring

In commutative algebra, a ring is said to be arithmetical (or arithmetic) if any of the following equivalent conditions hold: The localization of at is a uniserial ring for every maximal ideal of . For all ideals , and ,

For all ideals , and ,

The last two conditions both say that the lattice of all ideals of is distributive.

An arithmetical domain is the same thing as a Prüfer domain.

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