On matrix Lie rings over a commutative ring that contain the special linear Lie ring. (Q2798062)

Let \(K\) be an associative and commutative ring. Let \(G\) be a subring of the Lie ring \(\mathfrak{sl}_n(K)\) and suppose that \(G\) contains \(\mathfrak{sl}_n(k)\). Suppose further that \(n\geq 2\) is invertible in \(k\). The authors show that \(G=\mathfrak{sl}_n(L)\) where \(L\) is a subring of \(K\) that contains \(k\). Other results of this type are also shown and some examples are given.