The number of standard forms of matrices over imaginary Euclidean quadratic rings with respect to the $(z,k)$–equivalence
The $(z,k)$--equivalence of matrices over imaginary Euclidean quadratic rings is investigated. The classes of matrices over these rings are selected for which the standard form with respect to $(z,k)$--equivalence is uniquely defined and equal to the Smith normal form. It is established that the num...
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| Format: | Article |
| Language: | deu |
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Ivan Franko National University of Lviv
2022-06-01
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| Series: | Математичні Студії |
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| Online Access: | http://matstud.org.ua/ojs/index.php/matstud/article/view/287 |
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| author | N. B. Ladzoryshyn V. M. Petrychkovych |
| author_facet | N. B. Ladzoryshyn V. M. Petrychkovych |
| author_sort | N. B. Ladzoryshyn |
| collection | DOAJ |
| description | The $(z,k)$--equivalence of matrices over imaginary Euclidean
quadratic rings is investigated. The classes of matrices over
these rings are selected for which the standard form with respect
to $(z,k)$--equivalence is uniquely defined and equal to the Smith
normal form. It is established that the number of standard forms
over imaginary Euclidean quadratic rings is finite. Bounds for a
number of standard forms are established. |
| format | Article |
| id | doaj-art-ee11e249344e469d82d7b372fca29f5a |
| institution | DOAJ |
| issn | 1027-4634 2411-0620 |
| language | deu |
| publishDate | 2022-06-01 |
| publisher | Ivan Franko National University of Lviv |
| record_format | Article |
| series | Математичні Студії |
| spelling | doaj-art-ee11e249344e469d82d7b372fca29f5a2025-08-20T02:41:29ZdeuIvan Franko National University of LvivМатематичні Студії1027-46342411-06202022-06-0157211512110.30970/ms.57.2.115-121287The number of standard forms of matrices over imaginary Euclidean quadratic rings with respect to the $(z,k)$–equivalenceN. B. Ladzoryshyn0V. M. Petrychkovych1Pidstryhach Institute for Applied Problems of Mechanics and Mathematics NAS of Ukraine Lviv, UkrainePidstryhach Institute for Applied Problems of Mechanics and Mathematics NAS of UkraineThe $(z,k)$--equivalence of matrices over imaginary Euclidean quadratic rings is investigated. The classes of matrices over these rings are selected for which the standard form with respect to $(z,k)$--equivalence is uniquely defined and equal to the Smith normal form. It is established that the number of standard forms over imaginary Euclidean quadratic rings is finite. Bounds for a number of standard forms are established.http://matstud.org.ua/ojs/index.php/matstud/article/view/287quadratic ring; equivalence of a matrix; (z, k)–equivalence; standard form |
| spellingShingle | N. B. Ladzoryshyn V. M. Petrychkovych The number of standard forms of matrices over imaginary Euclidean quadratic rings with respect to the $(z,k)$–equivalence Математичні Студії quadratic ring; equivalence of a matrix; (z, k)–equivalence; standard form |
| title | The number of standard forms of matrices over imaginary Euclidean quadratic rings with respect to the $(z,k)$–equivalence |
| title_full | The number of standard forms of matrices over imaginary Euclidean quadratic rings with respect to the $(z,k)$–equivalence |
| title_fullStr | The number of standard forms of matrices over imaginary Euclidean quadratic rings with respect to the $(z,k)$–equivalence |
| title_full_unstemmed | The number of standard forms of matrices over imaginary Euclidean quadratic rings with respect to the $(z,k)$–equivalence |
| title_short | The number of standard forms of matrices over imaginary Euclidean quadratic rings with respect to the $(z,k)$–equivalence |
| title_sort | number of standard forms of matrices over imaginary euclidean quadratic rings with respect to the z k equivalence |
| topic | quadratic ring; equivalence of a matrix; (z, k)–equivalence; standard form |
| url | http://matstud.org.ua/ojs/index.php/matstud/article/view/287 |
| work_keys_str_mv | AT nbladzoryshyn thenumberofstandardformsofmatricesoverimaginaryeuclideanquadraticringswithrespecttothezkequivalence AT vmpetrychkovych thenumberofstandardformsofmatricesoverimaginaryeuclideanquadraticringswithrespecttothezkequivalence AT nbladzoryshyn numberofstandardformsofmatricesoverimaginaryeuclideanquadraticringswithrespecttothezkequivalence AT vmpetrychkovych numberofstandardformsofmatricesoverimaginaryeuclideanquadraticringswithrespecttothezkequivalence |