Let 
be a ring. If 
is a ring homomorphism,
then 
is an ideal of 
, 
is a subring of 
, and 
.
First Ring Isomorphism Theorem
See also
Second Ring Isomorphism Theorem, Third Ring Isomorphism Theorem, Fourth Ring Isomorphism TheoremThis 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, 2003.Referenced on Wolfram|Alpha
First Ring Isomorphism TheoremCite this as:
Hutzler, Nick. "First Ring Isomorphism Theorem." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/FirstRingIsomorphismTheorem.html