Description: Let the interval $I=[0,1]$ in the real numbers be a monoid under addition, where $a+b:=0$ if $a+b >1$. The ring is the monoid ring of $I$ over the field $F_2$ of two elements.

Notes: $J(R)$ is idempotent and nil.

Keywords semigroup ring

Reference(s):

- C. Hajarnavis and N. Norton. On dual rings and their modules. (1985) @ Example 6.2, pp 265-266
- N. C. Norton. Generalizations of the theory of quasi-frobenius rings. (1975) @ Example 3.2.2, p 112

Known Properties

Legend

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

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

cardinality | $\mathfrak c$ | |

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

Krull dimension (classical) | 0 |

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

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