Let 
be a ring, and let 
be an ideal of 
. The correspondence 
is an inclusion preserving bijection between the
set of subrings 
of 
that contain 
and the set of subrings of 
. Furthermore, 
(a subring containing 
) is an ideal of 
iff 
is an ideal of 
.
Fourth Ring Isomorphism Theorem
See also
First Ring Isomorphism Theorem, Second Ring Isomorphism Theorem, Third Ring Isomorphism TheoremThis 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
Fourth Ring Isomorphism TheoremCite this as:
Hutzler, Nick. "Fourth Ring Isomorphism Theorem." From MathWorld--A Wolfram Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/FourthRingIsomorphismTheorem.html