Assume that $\mathbb{F}$ is a field, and let $\mathbb{M}_{t}\left( \mathbb{F}\right) $ be the ring of matrices of order $t$ over $\mathbb{F}$.
Does there exist a non-trivial ring homomorphism from $\mathbb{M}_{n+1}\left( \mathbb{F}\right) $ to $\mathbb{M}_{n}\left( \mathbb{F}\right) $?