Linear group over a class of ring R (Q1061856)

We extend the results of \textit{D. Djoković} and \textit{J. Malzan} [Linear Algebra Appl. 28, 53-62 (1979; Zbl 0419.20037)] to a class of rings R, give the symmetric generation theorem for \(GL_ n(R)\) and a method for constructing symmetric factors. The method of this paper also can be applied to the discussion for the length of transvection-generation of \(GL_ n(R)\). In particular, all the results of this paper still hold if the ring R are replaced by a \(\Phi\)-surjective ring.