Journal of Mathematical Sciences

, Volume 219, Issue 4, pp 513–518 | Cite as

Decomposition of Elementary Transvection in Elementary Group

  • R. Y. Dryaeva
  • V. A. Koibaev

Let σ = (σij ) be an elementary net (elementary carpet) of additive subgroups of a commutative ring (in other words, a net without diagonal), n the order of σ, ω = (ωij ) the derived net with respect to σ, and Ω = (Ωij ) the net associated with the elementary group E(σ). It is assumed that ω ⊆ σ ⊆ Ω and Ω is the smallest (complemented) net containing σ. The main result consists in finding the decomposition of any elementary transvection tij(α) into the product of two matrices M 1 ∈ 〈t ij (σ ij ), t ji (σ ji )〉 and M2 ∈ G(τ), where \( \uptau =\left(\begin{array}{ll}{\varOmega}_{11}\hfill & {\upomega}_{12}\hfill \\ {}{\upomega}_{21}\hfill & {\varOmega}_{22}\hfill \end{array}\right) \).


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© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.North-Ossetian State UniversityVladicaucasusRussia
  2. 2.North-Ossetian State University, South Mathematical Institute of the Russian Academy of SciencesVladicaucasusRussia

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