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Sib. Èlektron. Mat. Izv., 2019, Volume 16, Pages 165–174 (Mi semr1047)  

Mathematical logic, algebra and number theory

A criterion for the universality of a matrix from the group $UT_n(R)$ over a commutative and associative ring $R$ with unity

N. G. Khisamiev, S. D. Tynybekova, A. A. Konyrkhanova

Faculty of Information Technologies, 2, Satpayev str., Astana, 010008, Kazakhstan

Abstract: We find necessary and sufficient universality conditions of a matrix from the unitriangular matrix group of arbitrary finite dimension over a commutative associative ring with unity. An algorithm is used to determine the universality of the element of the unitriangular matrix group over the ring of polynomials with a finite number of variables with integer coefficients.

Keywords: unitriangular matrix group, derived subgroup, universal element, ring, Euclidean ring.

Funding Agency Grant Number
Ministry of Education and Science of the Republic of Kazakhstan AP0513249


Full text: PDF file (152 kB)
References: PDF file   HTML file
UDC: 512.54
MSC: 20F18,20H25
Received June 12, 2017, published February 6, 2019

Citation: N. G. Khisamiev, S. D. Tynybekova, A. A. Konyrkhanova, “A criterion for the universality of a matrix from the group $UT_n(R)$ over a commutative and associative ring $R$ with unity”, Sib. Èlektron. Mat. Izv., 16 (2019), 165–174

Citation in format AMSBIB
\Bibitem{KhiTynKon19}
\by N.~G.~Khisamiev, S.~D.~Tynybekova, A.~A.~Konyrkhanova
\paper A criterion for the universality of a matrix from the group $UT_n(R)$ over a commutative and associative ring $R$ with unity
\jour Sib. \`Elektron. Mat. Izv.
\yr 2019
\vol 16
\pages 165--174
\mathnet{http://mi.mathnet.ru/semr1047}


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