Let $M$ be the additive submonoid of nonnegative rationals generated by $\frac{1}{2^ip_i}$ for $i \geq 0$, where $\{p_i\mid i\in\mathbb N\}$ is an enumeration of the odd primes of $\mathbb N$. With a field $k$ and indeterminate $X$, consider the $k$ algebra $S$ generated by $\{X^m \mid m\in M\}$. The required ring is $S$ localized at the set of elements with nonzero constant term.
Keywords semigroup ring
| Name | Measure | |
|---|---|---|
| cardinality | $\aleph_0$ | |
| composition length | left: $\infty$ | right: $\infty$ |
| Name | Description |
|---|---|
| Idempotents | $\{0,1\}$ |
| Left singular ideal | $\{0\}$ |
| Left socle | $\{0\}$ |
| Nilpotents | $\{0\}$ |
| Right singular ideal | $\{0\}$ |
| Right socle | $\{0\}$ |
| Zero divisors | $\{0\}$ |