Statements (18)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:alsoKnownAs |
Fundamental Homomorphism Theorem
|
| gptkbp:appliesTo |
groups
modules rings |
| gptkbp:category |
isomorphism theorem
|
| gptkbp:field |
abstract algebra
|
| https://www.w3.org/2000/01/rdf-schema#label |
First Isomorphism Theorem
|
| gptkbp:implies |
the image of a homomorphism is isomorphic to the quotient by its kernel
|
| gptkbp:introduced |
gptkb:Emmy_Noether
|
| gptkbp:relatedTo |
gptkb:Second_Isomorphism_Theorem
gptkb:Third_Isomorphism_Theorem |
| gptkbp:state |
If φ: G → H is a group homomorphism, then G/ker(φ) ≅ im(φ).
|
| gptkbp:usedIn |
group theory
module theory ring theory |
| gptkbp:bfsParent |
gptkb:lattice_isomorphism_theorem
|
| gptkbp:bfsLayer |
8
|