Noether isomorphism theorems

GPTKB entity

Predicate	Object
gptkbp:instanceOf	gptkb:mathematical_concept
gptkbp:alsoKnownAs	isomorphism theorems
gptkbp:appliesTo	groups modules rings
gptkbp:field	abstract algebra
gptkbp:firstTheorem	gptkb:First_isomorphism_theorem
gptkbp:firstTheoremStatement	If f: G → H is a group homomorphism, then G/ker(f) ≅ im(f).
https://www.w3.org/2000/01/rdf-schema#label	Noether isomorphism theorems
gptkbp:importantFor	fundamental in algebra
gptkbp:introduced	gptkb:Emmy_Noether
gptkbp:namedAfter	gptkb:Emmy_Noether
gptkbp:numberOfTheorems	three
gptkbp:relatedTo	gptkb:illustrator gptkb:operating_system homomorphism subfamily normal subgroup quotient structure
gptkbp:secondTheorem	gptkb:Second_isomorphism_theorem
gptkbp:secondTheoremStatement	If A and B are subgroups of G, then (A·B)/B ≅ A/(A∩B).
gptkbp:thirdTheorem	Third isomorphism theorem
gptkbp:thirdTheoremStatement	If N ⊆ H ⊆ G with N normal in G, then (G/N)/(H/N) ≅ G/H.
gptkbp:usedIn	group theory module theory ring theory
gptkbp:bfsParent	gptkb:Amalie_Emmy_Noether
gptkbp:bfsLayer	5