Arithmetical ring
In algebra, a commutative ring R is said to be arithmetical (or arithmetic) 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.

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Ring theory