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

- F. Rohrer. Irreducibility and integrity of schemes. (2015) @ Item 1.11 p 5

Known Properties

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

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

cardinality | $\aleph_0$ |

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

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

Jacobson radical | $\{0\}$ |

Left singular ideal | $\{0\}$ |

Nilpotents | $\{0\}$ |

Right singular ideal | $\{0\}$ |

Units | $\mathbb Q$ |