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On the Latimer-MacDuffee theorem for polynomials over finite fields
Thesis (PhD (Mathematical Sciences))--University of Stellenbosch, 2011.
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| Format: | Thesis |
| Language: | English |
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Stellenbosch : University of Stellenbosch
2011
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| _version_ | 1867614008803065857 |
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| access_status_str | Open Access |
| author | Van Zyl, Jacobus Visser |
| author2 | Breuer, Florian |
| author_browse | Breuer, Florian Van Zyl, Jacobus Visser |
| author_facet | Breuer, Florian Van Zyl, Jacobus Visser |
| author_sort | Van Zyl, Jacobus Visser |
| collection | Thesis |
| dc_rights_str_mv | University of Stellenbosch |
| description | Thesis (PhD (Mathematical Sciences))--University of Stellenbosch, 2011. |
| format | Thesis |
| id | oai:scholar.sun.ac.za:10019.1/6581 |
| institution | Stellenbosch University (South Africa) |
| language | English |
| last_indexed | 2026-06-10T12:45:13.015Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from SUNScholar — Stellenbosch University Repository |
| publishDate | 2011 |
| publishDateRange | 2011 |
| publishDateSort | 2011 |
| publisher | Stellenbosch : University of Stellenbosch |
| publisherStr | Stellenbosch : University of Stellenbosch |
| record_format | dspace |
| source_str | SUNScholar — Stellenbosch University Repository |
| spelling | oai:scholar.sun.ac.za:10019.1/6581 On the Latimer-MacDuffee theorem for polynomials over finite fields Van Zyl, Jacobus Visser Breuer, Florian University of Stellenbosch. Faculty of Science. Dept. of Mathematical Sciences. Matrices Polynomials over a finite field Ideal classes Class groups Dissertations -- Mathematics Theses -- Mathematics Equivalence classes of matrices Equivalence classes of ideals Latimer-MacDuffee theorem Thesis (PhD (Mathematical Sciences))--University of Stellenbosch, 2011. Includes bibliography. ENGLISH 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. AFRIKAANSE 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. Doctoral 2011-02-28T10:55:51Z 2011-03-14T08:21:18Z 2011-02-28T10:55:51Z 2011-03-14T08:21:18Z 2011-03 Thesis http://hdl.handle.net/10019.1/6581 en University of Stellenbosch 44 p. application/pdf Stellenbosch : University of Stellenbosch |
| spellingShingle | Matrices Polynomials over a finite field Ideal classes Class groups Dissertations -- Mathematics Theses -- Mathematics Equivalence classes of matrices Equivalence classes of ideals Latimer-MacDuffee theorem Van Zyl, Jacobus Visser On the Latimer-MacDuffee theorem for polynomials over finite fields |
| title | On the Latimer-MacDuffee theorem for polynomials over finite fields |
| title_full | On the Latimer-MacDuffee theorem for polynomials over finite fields |
| title_fullStr | On the Latimer-MacDuffee theorem for polynomials over finite fields |
| title_full_unstemmed | On the Latimer-MacDuffee theorem for polynomials over finite fields |
| title_short | On the Latimer-MacDuffee theorem for polynomials over finite fields |
| title_sort | on the latimer macduffee theorem for polynomials over finite fields |
| topic | Matrices Polynomials over a finite field Ideal classes Class groups Dissertations -- Mathematics Theses -- Mathematics Equivalence classes of matrices Equivalence classes of ideals Latimer-MacDuffee theorem |
| url | http://hdl.handle.net/10019.1/6581 |
| work_keys_str_mv | AT vanzyljacobusvisser onthelatimermacduffeetheoremforpolynomialsoverfinitefields |