explicite description of the relative infinite elementary linear group
Proposition
Let \(R\) be a ring, \(\mathfrak{a} \subseteq R\) an ideal
Then the relative infinite elementary linear group \(E(R, \mathfrak{a})\) is given by the normal closure of the elementary matrices \(e_{i,j}(a)\) with \(a \in \mathfrak{a}\)