  Let $R$ be the polydisc algebra or the Wiener algebra. It is shown that the
group $SL_n(R)$ is generated by the subgroup of elementary matrices with all
diagonal entries $1$ and at most one nonzero off-diagonal entry. The result an
easy consequence of the deep result due to Ivarsson and Kutzschebauch (Ann. of
Math. 2012).

Commutative Algebra;Complex Variables;Functional Analysis