Description: 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

Reference(s):

- A. Grams. Atomic rings and the ascending chain condition for principal ideals. (1974) @ Main example

Known Properties

Legend

- = has the property
- = does not have the property
- = information not in database

Name | Measure | |
---|---|---|

cardinality | $\aleph_0$ | |

composition length | left: $\infty$ | right: $\infty$ |

Name | Description |
---|---|

Idempotents | $\{0,1\}$ |

Nilpotents | $\{0\}$ |

Zero divisors | $\{0\}$ |