Let $M$ be a monoid generated by $y$, $x_i$, $i\in \mathbb Z$ subject to the relations $yx_i=x_{i-1}$. The ring $R$ is the monoid ring $\mathbb Q[M]$.
Keywords semigroup ring
| Name | Measure | |
|---|---|---|
| global dimension | left: | right: 1 |
| Name | Description |
|---|---|
| Idempotents | $\{0,1\}$ |
| Left singular ideal | $\{0\}$ |
| Left socle | $\{0\}$ |
| Nilpotents | $\{0\}$ |
| Right singular ideal | $\{0\}$ |
| Right socle | $\{0\}$ |
| Zero divisors | $\{0\}$ |