Date of Publication
9-1991
Document Type
Master's Thesis
Degree Name
Master of Science in Mathematics
Subject Categories
Curriculum and Instruction | Educational Assessment, Evaluation, and Research | Secondary Education
College
College of Science
Department/Unit
Mathematics and Statistics
Thesis Adviser
Blessilda Raposa
Defense Panel Chair
Aurora Trance
Defense Panel Member
Severino Diesto
Arlene Pascasio
Abstract/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.
Abstract Format
html
Language
English
Format
Accession Number
TG02036
Shelf Location
Archives, The Learning Commons, 12F Henry Sy Sr. Hall
Physical Description
90 leaves, 28 cm.
Keywords
Graph theory; Proof theory; Permutations
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Recommended Citation
Bagorio, B. L. (1991). Two approaches on the proof of the Amitsur-Levitzki theorem. Retrieved from https://animorepository.dlsu.edu.ph/etd_masteral/1414
