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Traceless matrices that are not commutators

Author: Ikuko Saito
Publisher: [Colorado Springs, Colorado] : University of Colorado Colorado Springs, 2015
Dissertation: M.S. University of Colorado Colorado Springs 2016
Edition/Format:   Thesis/dissertation : Document : Thesis/dissertation : eBook   Computer File : English
Database:WorldCat
Summary:
By a classical result, for any field F and a positive integer n, a matrix in M n (F) is a commutator if only and if it has trace zero. This is no longer true if F is replaced with an arbitrary ring R . But the only known examples of matrices which have trace zero and are not commutators are of the size 2 × 2. The purpose of this thesis is to construct an n × n matrix for any positive integer n e"2 which has trace  Read more...
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Details

Material Type: Document, Thesis/dissertation, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Ikuko Saito
OCLC Number: 958071265
Notes: Date of publication should read '2016'
Description: 1 online resource (iv, 21 pages)
Responsibility: by Ikuko Saito.

Abstract:

By a classical result, for any field F and a positive integer n, a matrix in M n (F) is a commutator if only and if it has trace zero. This is no longer true if F is replaced with an arbitrary ring R . But the only known examples of matrices which have trace zero and are not commutators are of the size 2 × 2. The purpose of this thesis is to construct an n × n matrix for any positive integer n e"2 which has trace zero but is not a commutator.

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