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