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Equivalence of pairs of matrices with relatively prime determinants over quadratic rings of principal ideals
Authors: Natalija Ladzoryshyn, Vasyl' Petrychkovych
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Abstract
A special equivalence of matrices and their pairs over quadratic rings is investigated. It is established that for the pair of $\, n\times n \, $ matrices $\, A,B \, $ over the quadratic rings of principal ideals $\, \mathbb{Z}[\sqrt{k}],$ where $\, (detA,detB)=1 \,$, there exist inver\-tible matri\-ces ${\, U\in GL(n,\mathbb{Z})\,} $ and $\, V^A,V^B\in GL(n,\mathbb{Z}[\sqrt{k}])$ such that $\, UAV^A=T^A \, $ and ${\, UBV^B=T^B \, }$ are the lower triangular matrices with invariant factors on the main $ {\mbox{diagonals.}}$Pidstryhach Institute for Applied Problems of Mechanics
and Mathematics of the NAS of Ukraine
3b Naukova Str., 79060, L’viv
Ukraine
E-mail: ,
and Mathematics of the NAS of Ukraine
3b Naukova Str., 79060, L’viv
Ukraine
E-mail: ,
Fulltext
– 0.14 Mb
Contents
- Estimates for the number of vertices with an interval spectrum in proper edge colorings of some graphs
- Closure operators in the categories of modules. Part IV (Relations between the operators and preradicals)
- Bi-Deniable Public-Key Encryption Protocol which is Secure against Active Coercive Adversary
- The endomorphism semigroup of a free dimonoid of rank 1
- Equivalence of pairs of matrices with relatively prime determinants over quadratic rings of principal ideals
- Limits of solutions to the singularly perturbed abstract hyperbolic-parabolic system
- On LCA groups with locally compact rings of continuous endomorphisms. I
- Algorithms for solving stochastic discrete optimal control problems on networks
- Near-totally conjugate orthogonal quasigroups
