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. 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