2 problems

Let $S$ be a congruence-simple semiring with a multiplicatively absorbing element $w$, and suppose that … for every $x\in S\setminus\{w\}$. Classification conjecture. If $S$ is fin…

Let $S$ and $S'$ be semirings with at least two elements and with bi-absorbing elements $o$ and $o'$, respectively. For the box-product $S\boxtimes S'$, write $V(G)$ for the semiri…