Thread: ideals

I have one problem with ideals. Which properties of ideal will cause that the factor ring is comutative or ring with 1?
Thanks

Originally Posted by sidi

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!

great......, thx bro