DECOMPOSITION OF ELEMENTARY TRANSVECTION IN ELEMENTARY GROUP

摘要

Let σ = (σ_(ij)) 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 = (ω_(ij)) the derived net with respect to σ, and Ω = (Ω_(ij)) the net associated with the elementary group E(σ). It is assumed that ω is contained in σ is contained in Ω and Ω is the smallest (complemented) net containing σ. The main result consists in finding the decomposition of any elementary transvection t_(ij) (α) into the product of two matrices M_1 ∈ and M_2 ∈ G(τ), where τ = (Ω_(11) ω_(12) ω_(21) Ω_(22). Bibliography. 5 titles.