Factorization of units and groups of stable homotopy equivalences
Let \(R\) be a ring with 1 and let \(R^*\) denote the group of units in \(R\). A subgroup \(G\) of \(R^*\) is said to be factorizable if \(G=A\cdot B\), where \(A,B\) are subgroups and \(A\cap B=(1)\). The author proves that if \(e\) is an idempotent and \(e+(1-e)G\subset G\) then \(G=(e+(1-e)G)\cdot((1-e)+eG)\) is a factorization. The factorization is a semi-direct product when at least one of the factors is normal in \(G\). The results are applied to computations of groups of stable homotopy equivalences.
scientific article; zbMATH DE number 1787475
scientific article