# Ring detail

## Name: Interval monoid ring

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 a field $F$.

Notes: $J(R)$ is idempotent and nil. Krull dimension $0$.

Keywords semigroup ring

Reference(s):

• Hajarnavis, C. R. ; Norton, N. C., On Dual Rings And Their Modules, Journal Of Algebra 93 P253-266, (1985). Example 6.2 P 265-266
• N. C. Norton, Generalizations Of The Theory Of Quasi-Frobenius Rings, Doctoral Dissertation For University Of Warwick, (1975). Example 3.2.2 P 112

This ring has the following properties:
The ring lacks the following properties:
We don't know if the ring has or lacks the following properties: