In mathematics, 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 an automorphism or nilpotent.[1]
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 a special case of the version above, since every K-linear representation of a group G can be viewed as a module over the group algebra KG.
In mathematics, the Fittinglemma – named after the mathematician Hans Fitting – is a basic statement in abstract algebra. Suppose M is a module over some...
for his work in group theory, particularly Fitting's theorem and the Fittinglemma. He died at the age of 31 from a bone disease. Witt was initially supervised...
group theory. He proved Fitting's theorem and Fitting'slemma, and defined the Fitting subgroup in finite group theory and the Fitting decomposition for Lie...
under an extension of a module by a simple module. For example, the Fittinglemma shows that the endomorphism ring of a finite length indecomposable module...
about endomorphisms of finite-length indecomposables is provided by the Fittinglemma. In the finite-length situation, decomposition into indecomposables...
Semidirect product Sylow theorems Hall subgroup Wreath product Butterfly lemma Center of a group Centralizer and normalizer Characteristic subgroup Commutator...
ring of an indecomposable module of finite length is local (e.g., by Fitting'slemma) and thus Azumaya's theorem applies to the setup of the Krull–Schmidt...
from the scalar ring R {\displaystyle R} . fitting 1. fitting ideal 2. Fitting'slemma five Five lemma flat A R {\displaystyle R} -module F {\displaystyle...
finite character has a maximal element with respect to inclusion (Tukey's lemma): In F {\displaystyle {\mathcal {F}}} , partially ordered by inclusion,...
distribution Reciprocal normal distribution Standard normal table Stein's lemma Sub-Gaussian distribution Sum of normally distributed random variables Tweedie...
(MICE). An alternative production method, Low Emittance Muon Accelerator (LEMMA) uses a positron beam impinging on a fixed target to produce muon pairs...
probability of Type I error is considered tolerable The Neyman-Pearson lemma states that this likelihood ratio test is the most powerful among all level-α...
lattice of subgroups of a group and that of its quotients. The Zassenhaus lemma gives an isomorphism between certain combinations of quotients and products...
Hilbert projection theorem, the separating hyperplane theorem, and Farkas' lemma.[citation needed] The convex programs easiest to solve are the unconstrained...
hypotheses List of inequalities Lists of integrals List of laws List of lemmas List of limits List of logarithmic identities List of mathematical functions...
Bartol, E. Orlowska & A. Skowran (1995) Helena Rasiowa, 1917 — 1994 Melvin Fitting (2006) A tribute to Helena Rasiowa Archived 2006-03-03 at the Wayback Machine...
former & titular see Joseph Lins, "Artvin" in The Catholic Encyclopedia lemma 'Artvin' in Catholic Encyclopedia (New York 1907) Artvin Village (in Turkish)...
For a perfect group, the UCS always stabilizes by the first step (Grün's lemma). However, a centerless group may have a very long LCS: a free group on...
interpretation. The word is also referred to by epiousios, its presumed lemma form. Since it is a Koine Greek dis legomenon (a word that occurs only twice...
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