Universal elements of unitriangular matrices groups

Assem Konyrkhanova, N. G. Khisamiev

2017

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DOI 10.31489/2017m2/79-85

Data confidence 70 medium

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Abstract

Universal elements of unitriangular matrices groupsThe 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.