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
Explore with Wolfram|Alpha
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
First Ring Isomorphism TheoremCite this as:
Hutzler, Nick. "First Ring Isomorphism Theorem." From MathWorld--A Wolfram Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/FirstRingIsomorphismTheorem.html