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Second Ring Isomorphism Theorem

Let R be a ring, let A be a subring, and let B be an ideal of R. Then A+B={a+b:a in A,b in B} is a subring of R, A intersection B is an ideal of A and

(A+B)/B=A/(A intersection B).

See also

First Ring Isomorphism Theorem, Third 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

Second Ring Isomorphism Theorem

Cite this as:

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

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