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 a field $k$ and indeterminate $X$, and generate $k$ algebra generated by $X^m$, $m\in M$. Localize at the set of elements with nonzero constant term. This localization is the ring.
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 | $\{0\}$ |