4 problems

Let $A$ be a PI-algebra over a field of characteristic zero, and let $c_n(A)$ denote the dimension of the space of multilinear polynomials of degree $n$ modulo the $T$-ideal of pol…

Bahturin–Zaicev's conjecture. The inequality

Let $\nu(n)$ be the minimal positive integer such that the polynomial $x_1\cdots x_{\nu(n)}$ belongs to the T-ideal generated by $x^n$; equivalently, $\nu(n)$ is the nilpotency ind…

Let $G$ be a finite abelian group and let $A$ be a $G$-graded PI-algebra. For each $k\geq 1$, write $\operatorname{GKdim}_k^G(A)$ for the $k$-th $\mathbb{Z}_2$-graded Gelfand–Kiril…