3 problems

Finite basis conjecture. The algebra $M_2(K)$ does not have a finite basis of its polynomial identities.

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…