Arithmetical ring

In algebra, a commutative ring R is said to be arithmetical if any of the following equivalent conditions hold:

The localization of R at is a uniserial ring for every maximal ideal of R.
For all ideals, and,
:
For all ideals, and,
:

The last two conditions both say that the lattice of all ideals of R is distributive.
An arithmetical domain is the same thing as a Prüfer domain.