On polynomials that are not quite an identity on an associative algebra

Eric Jespers, David Riley, Mayada Shahada

Let $f$ be a polynomial in the free algebra over a field $K$, and let $A$ be a $K$-algebra. We denote by ${\S }_A(f)$, $\A_A(f)$ and $\I_A(f)$, respectively, the `verbal' subspace, sub…