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Fourth Ring Isomorphism Theorem


Let R be a ring, and let I be an ideal of R. The correspondence A<->A/I is an inclusion preserving bijection between the set of subrings A of R that contain I and the set of subrings of R/I. Furthermore, A (a subring containing I) is an ideal of R iff A/I is an ideal of R/I.


See also

First Ring Isomorphism Theorem, Second Ring Isomorphism Theorem, Third Ring Isomorphism Theorem

This entry contributed by Nick Hutzler

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References

Dummit, D. S. and Foote, R. M. Abstract Algebra, 2nd ed. Englewood Cliffs, NJ: Prentice-Hall, p. 246, 2003.

Referenced on Wolfram|Alpha

Fourth Ring Isomorphism Theorem

Cite this as:

Hutzler, Nick. "Fourth Ring Isomorphism Theorem." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/FourthRingIsomorphismTheorem.html

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