5 problems

Park's conjecture. Every finitely generated variety of finite type that has a finite residual bound is finitely based.

HFB conjecture. The variety $\mathbb Q^1 \vee \mathbb L_3^1 \vee \mathbb R_3^1$ is hereditarily finitely based (HFB).

Let $K$ be an infinite field of characteristic $2$, and let $K^3$ be the three-dimensional simple Lie algebra equipped with the cross product. Nonfinite basis conjecture. The polyn…

Let $K$ be an infinite field of characteristic $2$, and let $M_2(K)$ denote the algebra of $2\times 2$ matrices. A polynomial identity basis is a finite set of polynomial identitie…

Let $G$ be a nilpotent group. A semigroup is periodic if every element generates a finite cyclic subsemigroup, and it is locally finite if each of its finitely generated subsemigro…