Let $L$ be the commutative semigroup with underlying set $\Bbb Q\times \Bbb N^{>0}$, where $(x,m)(y,n) = (x,m)$ when $x < y$, and $(x, m+n)$ if $x=y$. Adjoin a neutral element to $L$ and denote the resulting monoid by $M$. Then the ring is $R = \Bbb Q[M]$.
Keywords semigroup ring
| Name | Measure | |
|---|---|---|
| cardinality | $\aleph_0$ |
| Name | Description |
|---|---|
| Idempotents | $\{0,1\}$ |
| Jacobson radical | $\{0\}$ |
| Left singular ideal | $\{0\}$ |
| Nilpotents | $\{0\}$ |
| Right singular ideal | $\{0\}$ |
| Units | $\mathbb Q$ |