◀ ▲ ▶Branches / Algebra / Lemma: One-to-one Correspondence of Ideals in the Factor Ring and a Commutative Ring

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 \(I\).

Table of Contents

Proofs: 1

Mentioned in:

Proofs: 1

Thank you to the contributors under CC BY-SA 4.0!

Github:

non-Github:

@Brenner

References

Adapted from CC BY-SA 3.0 Sources:

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