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Third Ring Isomorphism Theorem

Let R be a ring, and let I and J be ideals of R with I subset= J. Then J/I is an ideal of R/I and

(R/I)/(J/I)=R/J.

See also

First Ring Isomorphism Theorem, Second Ring Isomorphism Theorem, Fourth Ring Isomorphism Theorem

This entry contributed by Nick Hutzler

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References

Dummit, D. S. and Foote, R. M. "Ring Homomorphisms and Quotient Rings." §7.3 in Abstract Algebra, 3rd ed. Hoboken, NJ: Wiley, pp. 239-250, 2004.

Referenced on Wolfram|Alpha

Third Ring Isomorphism Theorem

Cite this as:

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

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