Let $S$ be the semigroup of positive pairs of rationals under addition, along with $(0,0)$, and $k$ be a field (for concreteness we suppose the field of two elements, but any field works.) The semigroup algebra $R=k[S]$ is the required ring.
Keywords semigroup ring
(Nothing was retrieved.)
| Name | Description |
|---|---|
| Idempotents | $\{0,1\}$ |
| Left singular ideal | $\{0\}$ |
| Left socle | $\{0\}$ |
| Nilpotents | $\{0\}$ |
| Right singular ideal | $\{0\}$ |
| Right socle | $\{0\}$ |
| Zero divisors | $\{0\}$ |