2 problems

Let $K$ be the ground field, let $E$ denote the Grassmann algebra, and let $R$ be a PI-algebra with … where each $R_i$ is one of $K$, $E$, $M_2(K)$, or $E\otimes_K E$, and at least…

Let $K$ be the underlying field, let $M_k(K)$ denote the algebra of $k\times k$ matrices over $K$, and let $c(M_k(K),t)$ be its codimension series. For $k=2$, this series is algebr…