Nonfinite basis conjecture for polynomial identities of matrix algebras in characteristic two

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 identities from which all polynomial identities follow. Nonfinite basis conjecture. The polynomial identities of $M_2(K)$ do not follow from a finite number of identities. The text presents this as a conjecture because the corresponding case remains open, while contrasting it with the known nonfinite basis result for the related Lie algebra $gl_2(K)$.