# Commutative ring detail

## Name: Grams' atomic domain which doesn't satisfy ACCP

Description: Enumerate the primes in $\mathbb N$. Let $M$ be the additive submonoid of positive rationals generated by $\frac{1}{2^ip_i}$ $i \geq 0$. With field $F$ and indeterminate $X$, and generate $F$ algebra generated by $X^m$, $m\in M$. Localize at the set of elements with nonzero constant term. This localization is the ring.

Notes:

Keywords semigroup ring

Reference(s):

• Anne Grams, Atomic Rings And The Ascending Chain Condition For Principal Ideals., Math. Proc. Of The Cambridge Phil. Soc. Vol. 75. No. 03. Cambridge University., (1974). Main Example

This ring has the following properties:
The ring lacks the following properties:
We don't know if the ring has or lacks the following properties: