Ring $R_{ 51 }$

Description:

Using the field of two elements $F_2$, let $S=F_2[M]$ where $M$ is the monoid of nonnegative real numbers under addition. The required ring is $R=S/I$ where $I$ is the ideal generated by elements of $M$ greater than $1$. (The elements look like linear combinations of elements from the interval $[0,1]$.)

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

Keywords semigroup ring