Reduction of a pair of matrices to a special triangular form over a ring of almost stable range 1 (in Ukrainian)

Author S. I. Bilavska, I. S. Vasyunyk
mandaruna87@mail.ru, zosia_meliss@yahoo.co.uk
Ivan Franko National University of Lviv

Abstract In the paper it is considered a notion of a ring of almost stable range 1. It is shown that an arbitrary pair of matrices over commutative Bezout domain of almost stable range 1, where at least one of the matrices is not a zero divisor, reduced to a special triangular form with the corresponding elementary divisors on the main diagonal by using the unilateral transformations. It is also proved that elementary divisors of the product of matrices over a commutative Bezout domain of almost stable range 1 are elementary divisors of every multiplier.
Keywords matrices; triangular form; ring; stable range
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Pages 136-141
Volume 37
Issue 2
Year 2012
Journal Matematychni Studii
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