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

Thanks

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- May 11th 2009, 11:15 PMsidiideals
I have one problem with ideals. Which properties of ideal will cause that the factor ring is comutative or ring with 1?

Thanks - May 11th 2009, 11:51 PMNonCommAlg
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! - May 12th 2009, 02:06 AMadit38
great......, thx bro