Universal elements of unitriangular matrices groups
The following theorems are proved for a matrix g from the group of unitriangular matrices over a commutative and associative ring K of finite dimension of greater than three with unity: 1) if the matrix g is universal then all of its elements are on the first collateral diagonal except extreme ones...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Academician Ye.A. Buketov Karaganda University
2017-06-01
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| Series: | Қарағанды университетінің хабаршысы. Математика сериясы |
| Subjects: | |
| Online Access: | http://mathematics-vestnik.ksu.kz/index.php/mathematics-vestnik/article/view/162 |
| Summary: | The following theorems are proved for a matrix g from the group of unitriangular matrices over a commutative and associative ring K of finite dimension of greater than three with unity: 1) if the matrix g is universal then all of its elements are on the first collateral diagonal except extreme ones are nonzero; 2) if all elements of the first collateral diagonal of the matrix g , with the possible exception of the last element are reversible in K , then g is universal; 3) if the ring K is Euclidean and has no reversible elements except trivial ones, then it follows from the universality of the matrix g that all the elements of its first collateral diagonal, except the extreme ones, are reversible in K .
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| ISSN: | 2518-7929 2663-5011 |