Fitting lemma [SEP] named after
Fitting lemma
The Fitting lemma, named after the mathematician Hans Fitting, is a basic statement in abstract algebra. Suppose "M" is a module over some ring. If "M" is indecomposable and has finite length, then every endomorphism of "M" is either bijective or nilpotent.
As an immediate consequence, we see that the endomorphism ring of every finite-length indecomposable module is local.
A version of Fitting's lemma is often used in the representation theory of groups. This is in fact
lemma ("probability theory")
- Fekete's lemma ("mathematical analysis")
- Feld–Tai lemma ("electromagnetism")
- Finsler's lemma ("control theory")
- Fitting lemma ("abstract algebra")
- Five lemma ("homological algebra")
- Fixed-point lemma for normal functions ("axiomatic set theory")
- Fodor's lemma ("set theory")
- Forking lemma ("cryptography")
- Frattini's