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Journal of Siberian Federal University. Mathematics & Physics, 2012, Volume 5, Issue 3, Pages 388–392
(Mi jsfu254)
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This article is cited in 2 scientific papers (total in 2 papers)
Decomposition of transvection in elementary group
Vladimir A. Koibaevab a North-Ossetia State University, Vladikavkaz, Russia
b South Mathematical Institute of VSC RAS, Vladikavkaz, Russia
Abstract:
The elementary net (elementary carpet) $\sigma=(\sigma_{ij})$ an order 3 of additive subgroups commutative ring is considered, the derivative net $\omega$ connected with it, elementary group $E(\sigma)$ and net group $G(\omega)$. It is proved that a elementary transvection $t_{ij}(\alpha)$ from $E(\sigma)$ is a product of a matrix from group $\langle t_{ij}(\sigma_{ij}),t_{ji}(\sigma_{ji})\rangle$ and matrixes from $G(\omega)$.
Keywords:
net, carpet, elementary nets, net group, carpet group, elementary group, transvection.
Received: 22.12.2011 Received in revised form: 06.01.2012 Accepted: 10.03.2012
Citation:
Vladimir A. Koibaev, “Decomposition of transvection in elementary group”, J. Sib. Fed. Univ. Math. Phys., 5:3 (2012), 388–392
Linking options:
https://www.mathnet.ru/eng/jsfu254 https://www.mathnet.ru/eng/jsfu/v5/i3/p388
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