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

Geodesic

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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

Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 165-174

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Résumé

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.

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

@article{SEMR_2019_16_a1,
     author = {N. G. Khisamiev and S. D. Tynybekova and A. A. Konyrkhanova},
     title = {A criterion for the universality of a matrix from the group $UT_n(R)$ over a commutative and associative ring $R$ with unity},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {165--174},
     publisher = {mathdoc},
     volume = {16},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2019_16_a1/}
}

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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. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 165-174. http://geodesic.mathdoc.fr/item/SEMR_2019_16_a1/