5 problems

Let $M_n(K)$ be the algebra of $n\times n$ matrices over a field $K$ of characteristic $0$, and let $\operatorname{mindeg}(M_n(K))$ denote the minimal degree of a central polynomia…

Let $K$ be a field and let $M_d(K)$ denote the algebra of $d\times d$ matrices. A central polynomial is a polynomial that takes only central values on $M_d(K)$ but is not a polynom…

Let $F$ be the base field and let $M_k(F)$ be the algebra of $k\times k$ matrices. A non-identity central polynomial for $M_k(F)$ is a polynomial whose evaluations are scalar matri…

Let $A$ be a PI algebra, and let $\delta_n(A)$ denote the $n$th codimension sequence associated with its central polynomials. For ordinary codimensions, Giambruno and Zaicev proved…

Let $F$ be the base field and let $M_k(F)$ be the algebra of $k\times k$ matrices. Write $c_n(M_k(F))$ for its $n$th codimension and $c_n^z(M_k(F))$ for the corresponding codimensi…