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Let $H_n$ denote the set of $n \times n$ nilpotent matrices with complex entries. The set $H_n$ may be regarded as an algebraic variety. Indeed, consider the polynomial ring $\mathbb{C}[A_{i,j} : 1 \...

Let $F$ be a finite field, $R=F[x]$ be a polynomial ring and $K = \mathrm{Mat}_n(R)$ be a full matrix ring over $R$. We identify the ring $K$ with the ring $\mathrm{Mat}_n(F)[x]$, for example $$ \left(...