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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Main Author:	Bagorio, Bernardo L.
Format:	text
Language:	English
Published:	Animo Repository 1991
Subjects:	Graph theory Proof theory Permutations Curriculum and Instruction Educational Assessment, Evaluation, and Research Secondary Education
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

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spelling	oai:animorepository.dlsu.edu.ph:etd_masteral-82522022-03-08T05:39:15Z Two approaches on the proof of the Amitsur-Levitzki theorem Bagorio, Bernardo L. 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. 1991-09-01T07:00:00Z text application/pdf https://animorepository.dlsu.edu.ph/etd_masteral/1414 https://animorepository.dlsu.edu.ph/context/etd_masteral/article/8252/viewcontent/TG02036_F_Redacted.pdf Master's Theses English Animo Repository Graph theory Proof theory Permutations Curriculum and Instruction Educational Assessment, Evaluation, and Research Secondary Education
institution	De La Salle University
building	De La Salle University Library
continent	Asia
country	Philippines Philippines
content_provider	De La Salle University Library
collection	DLSU Institutional Repository
language	English
topic	Graph theory Proof theory Permutations Curriculum and Instruction Educational Assessment, Evaluation, and Research Secondary Education
spellingShingle	Graph theory Proof theory Permutations Curriculum and Instruction Educational Assessment, Evaluation, and Research Secondary Education Bagorio, Bernardo L. Two approaches on the proof of the Amitsur-Levitzki theorem
description	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.
format	text
author	Bagorio, Bernardo L.
author_facet	Bagorio, Bernardo L.
author_sort	Bagorio, Bernardo L.
title	Two approaches on the proof of the Amitsur-Levitzki theorem
title_short	Two approaches on the proof of the Amitsur-Levitzki theorem
title_full	Two approaches on the proof of the Amitsur-Levitzki theorem
title_fullStr	Two approaches on the proof of the Amitsur-Levitzki theorem
title_full_unstemmed	Two approaches on the proof of the Amitsur-Levitzki theorem
title_sort	two approaches on the proof of the amitsur-levitzki theorem
publisher	Animo Repository
publishDate	1991
url	https://animorepository.dlsu.edu.ph/etd_masteral/1414 https://animorepository.dlsu.edu.ph/context/etd_masteral/article/8252/viewcontent/TG02036_F_Redacted.pdf
_version_	1772835533936918528

Two approaches on the proof of the Amitsur-Levitzki theorem

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