Geodesic
Nets associated with the elementary nets
Vladikavkazskij matematičeskij žurnal, Tome 12 (2010) no. 4, pp. 39-43 
V. A. Koibaev. Nets associated with the elementary nets. Vladikavkazskij matematičeskij žurnal, Tome 12 (2010) no. 4, pp. 39-43. http://geodesic.mathdoc.fr/item/VMJ_2010_12_4_a5/
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     title = {Nets associated with the elementary nets},
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Voir la notice de l'article provenant de la source Math-Net.Ru

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

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