Lemma: One-to-one Correspondence of Ideals in the Factor Ring and a Commutative Ring

Let \(R\) be a commutative ring and let \(I\) be an ideal of the ring \(S=R/I\) being the resulting factor ring. Then there is a one-to-one correspondence of ideals of \(S\) and those of \(R\), which contain \(I\).

Proofs: 1

Proofs: 1

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Adapted from CC BY-SA 3.0 Sources:

  1. Brenner, Prof. Dr. rer. nat., Holger: Various courses at the University of Osnabrück