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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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 435, 2015, pp. 33–41.
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Dryaeva, R.Y., Koibaev, V.A. Decomposition of Elementary Transvection in Elementary Group. J Math Sci 219, 513–518 (2016). https://doi.org/10.1007/s10958-016-3123-4
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DOI: https://doi.org/10.1007/s10958-016-3123-4