10 problems

Let $S$ be the finite semigroup under consideration, let $u,u'\in S$, let $u^{{+}_r}$ and ${u'}^{{+}_l}$ denote their associated right and left idempotents, let $\boldsymbol{*}$ de…

Null-summand conjecture. There is some $m\ge 1$ such that $Z$ is a direct summand of $V^{\otimes m}$, and consequently

Let … be a Burnside semigroup, and for $s\in\mathcal{B}(m,n)$ let $S^{\mathscr{J}}_s$ be the finite semigroup formed by the elements $\mathscr{J}$-above $s$, together with zero…

Let $(S,A)$ be a finite semigroup with generating set $A$, and let $\mathsf{KR}(S,A)$ and $\mathsf{Mc}$ denote the Karnofsky–Rhodes and McCammond expansions, respectively. The expa…

Let $S$ be a finite semigroup with generating set $A$, let $(\mathsf{KR}(S,A),A)$ be its Karnofsky–Rhodes expansion, and let $K(\mathsf{KR}(S,A))$ be a Kleene expression for its no…

Let $p>2$ be a prime, let $f(x)\in \mathbb{F}_p[x]$ be a non-constant polynomial, and let $\mathcal{S}_{f(x)}^p$ denote the multiplicative semigroup of the quotient ring…

Let $\Gamma$ be a finite directed acyclic graph. Its universal dynamics monoid $D(\Gamma)$ is the smallest quotient of $\operatorname{\mathbf{HK}}_\Gamma$ through which all evaluat…

Erdős–Ginzburg–Ziv conjecture for semigroups. For any finite commutative semigroup $\mathcal{S}$,

Subsemigroup conjecture. If $S$ is not adequate, then $S$ contains a subsemigroup isomorphic to $M$.

Let $M$ be the finite monoid under consideration, let $X$ be its generating alphabet, let $R$ be the relevant set on which $\Omega(X)$ acts, and let $P(M)$ denote the power set of…