Geodesic
Nets associated with the elementary nets
Vladikavkazskij matematičeskij žurnal, Tome 12 (2010) no. 4, pp. 39-43 Cet article a éte moissonné depuis la source Math-Net.Ru

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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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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/

[1] Borevich Z. I., “O podgruppakh lineinykh grupp, bogatykh transvektsiyami”, Zap. nauch. seminarov LOMI, 75, 1978, 22–31 | MR | Zbl

[2] Kargapolov M. I., Merzlyakov Yu. I., Osnovy teorii grupp, Nauka, M., 1982, 288 pp. | MR | Zbl

[3] Levchuk V. M., “Zamechanie k teoreme L. Diksona”, Algebra i logika, 22:5 (1983), 504–517 | MR | Zbl

[4] Kourovskaya tetrad. Nereshennye voprosy teorii grupp, 17-e, dopolnennoe, IM SO RAN, Novosibirsk, 2010, 219 pp.