Parabolic factorization for a matrix ring

In the present paper, we prove Dennis–Vaserstein type decomposition (or a parabolic factorization) for some pairs of parabolic subsets $P_r$ and $\mathrm{MP}_s$ in the matrix ring $M(n,R)$ over Hermite ring $R$. We also formulate and prove analogous results for non-square matrices.