I have one problem with ideals. Which properties of ideal will cause that the factor ring is comutative or ring with 1?
Thanks
first has to be a two sided ideal because otherwise the factor ring wouldn't be defined. now commutativity of means that for all i.e.
so is commutative iff contains all additive commutators. for to have 1, there must exist such that for all
or equivalently and you can't put this condition in a more familiar form!