3 problems

Let $\mathbb{F}$ be the semiring of functional digraphs, with multiplication given by the product of functional digraphs. A functional digraph $X\in\mathbb{F}$ is prime if…

Let $\mathbb{N}[x]$ be the polynomial semiring with coefficients in $\mathbb{N}$, and let $\mathbb{N}[x]=C_0\cup C_1$ be a bipartition. The polynomial semiring conjecture. There ex…

Perfectness conjecture. In the class of all additively regular semirings, perfect semirings are precisely perfect rings.