The Amitsur-Levitzki theorem is a result in algebra concerning the algebra of n by n matrices over a commutative ring. It states that this algebra satisfies a specific polynomial identity of degree 2n, and that this identity is the minimal one such matrix rings satisfy, so matrix rings are examples of polynomial identity rings. The theorem was established by Shimshon Amitsur and Jacob Levitzki in 1950. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/
Facts
StatementThe algebra of n by n matrices over a commutative ring satisfies a polynomial identity of degree 2n, and no identity of smaller degree holds for all such matrices. 1 Classification
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Source Amitsur-Levitzki theorem (Wikipedia)
Proved By
Source Amitsur-Levitzki Theorem (Wikipedia)
Source Amitsur-Levitzki Theorem (Wikipedia)
Sources
1. Amitsur-Levitzki theorem (Wikipedia)
Proofs section
Amitsur and Levitzki (1950) gave the first proof.
- In Branch: Algebra, Lead sentence
In Group: Ring Theory and Commutative Algebra, Lead section
by Amitsur and Levitsky (1950). In particular matrix rings are polynomial identity rings such that the smallest
View the SourceAmitsur-Levitzki Theorem (Wikipedia)
Proved By: Shimshon Amitsur, Lead sentence, attribution
It was proved by Amitsur and Levitsky (1950)
Proved By: Jakob Levitzki, Lead sentence, attribution
It was proved by Amitsur and Levitsky (1950)
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