Two approaches on the proof of the Amitsur-Levitzki theorem
In Minimal identities for Algebras by Amitsur and Levitzki, which appeared in the Proceedings of the American Mathematical Society (1950), the Amitsur-Levitzki Theorem states that If A1, A2, . . . . , A2n are any n x n matrices with entries in any commutative ring, then[A1, . . . . , A2n] = 0where [...
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| Format: | text |
| Language: | English |
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Animo Repository
1991
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| Online Access: | https://animorepository.dlsu.edu.ph/etd_masteral/1414 https://animorepository.dlsu.edu.ph/context/etd_masteral/article/8252/viewcontent/TG02036_F_Redacted.pdf |
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| Institution: | De La Salle University |
| Language: | English |
| Summary: | In Minimal identities for Algebras by Amitsur and Levitzki, which appeared in the Proceedings of the American Mathematical Society (1950), the Amitsur-Levitzki Theorem states that If A1, A2, . . . . , A2n are any n x n matrices with entries in any commutative ring, then[A1, . . . . , A2n] = 0where [A1, . . . . , A2n] = sgn (0) A0(1) A 0(2) . . . A0(2n) where the sum is taken over all permutations 0 of the integers 1, 2, . . . , 2n.In this thesis, the author presents two proofs of the above-mentioned theorem in an extensive, comprehendible and detailed manner. The first proof was constructed by Amitsur and Levitzki using abstract algebra and linear algebra, while the second proof utilizes concepts in graph theory. |
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