A set of theorems describing how quotients, subgroups (or submodules) and homomorphisms interact, formalized in the generality of abstract algebra by Emmy Noether. They are among the most frequently invoked structural results across group, ring and module theory.
Facts
StatementThe isomorphism theorems describe how quotients, subgroups or submodules, and homomorphisms interact: the first theorem states that the image of a homomorphism is isomorphic to the quotient of its domain by its kernel, and the second and third describe corresponding isomorphisms among quotients formed from a subobject and a normal subobject or from nested quotients. 1 Classification
Statement FormCharacterization Theorem 1 Connections
In Branch
Named After
Derived from the theorem's own name (unambiguous possessive-token match to exactly one live mathematician entity, w-bfill-g5-0924 browse backfill)
Proved By
Sources
1. Noether's isomorphism theorems (Wikipedia)
Wikimedia FoundationIntroduction
the isomorphism theorems (also known as Noether's isomorphism theorems) are theorems that describe the relationship among quotients, homomorphisms, and subobjects
History section
The isomorphism theorems were formulated in some generality for homomorphisms of modules by Emmy Noether in her paper Abstrakter Aufbau der Idealtheorie in algebraischen Zahl- und Funktionenkörpern, which was published in 1927 in Mathematische Annalen.
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