define a finite semiring
What would be the simplest way to define the semiring with elements $\{0, 1\}$ with the logical OR ($|$) operation as addition and the standard integer multiplication?
At very least it should be accepted by PolynomialRing
as the domain for coefficients.
Is this
GF(2)
?No. In $GF(2)$ we have $1+1=0$, while here $1+1=1$.