Nets associated with the elementary nets

For an elementary net (i.~e. a net without diagonal) $\sigma = (\sigma_{ij})$ of additive subgroups $\sigma_{ij}$, $i\neq{j},$ of a commutative ring $R$ with 1 two nets are constructed: the net $\omega_{\sigma}$ associated with $\sigma$ and the net $\Omega^{\sigma}$ as\-so\-ciated with the elementary group $E(\sigma)$, and (on the off-diagonal positions) we have $\omega_{\sigma}\subseteq{\sigma}\subseteq{\Omega^{\sigma}}$.