This article is cited in 12 papers

Nets associated with the elementary nets

V. A. Koibaev<sup>ab

a</sup> North-Ossetia State University, Russia, Vladikavkaz
^b South Mathematical Institute of VSC RAS, Russia, Vladikavkaz

Abstract: 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 $\omega_\sigma\subseteq\sigma\subseteq\Omega^\sigma$.

Key words: nets, net groups, elementary group, transvection.

UDC: 519.46

Received: 15.10.2010