5 problems

For a numerical semigroup $S$, let $g(S)$ denote its genus and, for each $r\in\mathbb{N}_0$, let … where $\widetilde{\Delta}=\Delta\cup\{0\}$ is the numerical semigroup associated…

Bound conjecture. There exists a semimodule $\Delta$ minimally generated by $[0,g]$ for a gap $g$ of $\Gamma$, such that

Let $G=B_1\cup\dotsm\cup B_q$ be a finite partition of a semimodule $(G,\pmb{+})$ over a semiring $(R,+,\cdot)$. For a subset $F\subseteq R$, write $Fb=\{fb:f\in F\}$. Schur–Brauer…

Let $(R,\vee,\circ)$ be a finite simple additively idempotent semiring with an absorbing greatest element, and suppose it possesses a finite idempotent irreducible semimodule witho…

Let $(R,+,\cdot)$ be a finite, simple, additively idempotent semiring, and let $(M,+)$ be a finite idempotent $R$-semimodule. A semimodule is sub-irreducible if it is non-quasitriv…