ITEM VIEW

On the Latimer-MacDuffee theorem for polynomials over finite fields

dc.contributor.advisorBreuer, Florian
dc.contributor.authorVan Zyl, Jacobus Visser
dc.contributor.otherUniversity of Stellenbosch. Faculty of Science. Dept. of Mathematical Sciences.
dc.date.accessioned2011-02-28T10:55:51Z
dc.date.accessioned2011-03-14T08:21:18Z
dc.date.available2011-02-28T10:55:51Z
dc.date.available2011-03-14T08:21:18Z
dc.date.issued2011-03
dc.identifier.urihttp://hdl.handle.net/10019.1/6581
dc.descriptionThesis (PhD (Mathematical Sciences))--University of Stellenbosch, 2011.
dc.descriptionIncludes bibliography.
dc.description.abstractENGLISH ABSTRACT: Latimer & MacDuffee showed in 1933 that there is a one-to-one correspondence between equivalence classes of matrices with a given minimum polynomial and equivalence classes of ideals of a certain ring. In the case where the matrices are taken over the integers, Behn and Van der Merwe developed an algorithm in 2002 to produce a representative in each equivalence class. We extend this algorithm to matrices taken over the ring Fq[T] of polynomials over a finite field and prove a modified version of the Latimer-MacDuffee theorem which holds for proper equivalence classes of matrices.en
dc.description.abstractAFRIKAANSE OPSOMMING: Latimer & MacDuffee het in 1933 bewys dat daar 'n een-tot-een korrespondensie is tussen ekwivalensieklasse van matrikse met 'n gegewe minimumpolinoom en ekwivalensieklasse van ideale van 'n sekere ring. In die geval waar die matrikse heeltallige inskrywings het, het Behn en Van der Merwe in 2002 'n algoritme ontwikkel om verteenwoordigers in elke ekwivalensieklas voort te bring. Ons brei hierdie algoritme uit na die geval van matrikse met inskrywings in die ring Fq[T] van polinome oor 'n eindige liggaam en ons bewys 'n gewysigde weergawe van die Latimer-MacDuffee stelling wat geld vir klasse van streng ekwivalente matrikse.af
dc.format.extent44 p.
dc.language.isoen
dc.publisherStellenbosch : University of Stellenbosch
dc.subjectMatricesen
dc.subjectPolynomials over a finite fielden
dc.subjectIdeal classesen
dc.subjectClass groupsen
dc.subjectDissertations -- Mathematicsen
dc.subjectTheses -- Mathematicsen
dc.subjectLatimer-MacDuffee theorem
dc.subjectEquivalence classes of matricesen
dc.subjectEquivalence classes of idealsen
dc.titleOn the Latimer-MacDuffee theorem for polynomials over finite fieldsen
dc.typeThesis
dc.rights.holderUniversity of Stellenbosch


Files in this item

Thumbnail
Thumbnail

This item appears in the following Collection(s)

ITEM VIEW