Prime and semiprime submodules of $R^n$ and a related Nullstellensatz for $M_n(R)$

Jaka Cimprič

Let $R$ be a commutative ring with $1$ and $n$ a natural number. We say that a submodule $N$ of $R^n$ is semiprime if for every $f=(f_1,\dots ,f_n)\in R^n$ such that $f_{i}f\in N$…