Decomposition of elementary transvection in elementary group

We consider the following data: an elementary net (or, what is the same elementary carpet) $\sigma=\sigma_{ij})$ of additive subgroups of a commutative ring (in other words, a net without the diagonal) of order $n$, a derived net $\omega=(\omega_{ij})$, which depends of the net $\sigma$, the net $\Omega=(\Omega_{ij})$, associated with the elementary group $E(\sigma)$, where $\omega\subseteq\sigma\subseteq\Omega$ and the net $\Omega$ is the smallest (complemented) net among the all nets which contain the elementary net $\sigma$. We prove that every elementary transvection $t_{ij}(\alpha)$ can be decomposed as a product of two matrices $M_1$ and $M_2$, where $M_1$ belongs to the group $\langle t_{ij}\sigma_{ij}),t_{ji}(\sigma_{ji})\rangle$, $M_2$ belongs to the net group $G(\tau)$ and the net $\tau$ has the form $\tau=\begin{pmatrix}\Omega_{11}&\omega_{12}
\omega_{21}&\Omega_{22}\end{pmatrix}$.