Romaniv A. Matrix divisors with prescribed canonical diagonal forms over polynomial and elementary divisor rings

Українська версія

Thesis for the degree of Candidate of Sciences (CSc)

State registration number

0415U000214

Thesis Registration Form

0415U000214.pdf

Applicant for

Specialization

  • 01.01.06 - Алгебра і теорія чисел

26-12-2014

Specialized Academic Board

К 20.051.09

Kolomyia Educational-Scientific Institute The Vasyl Stefanyk Precarpathian National University

Essay

The dissertation is devoted to the research of matrix factorizations over various classes of commutative elementary divisor domains. There are established the necessary and sufficient conditions for separate a monic divisor from the polynomial matrix over the infinite field. As a consequence we have obtained the relationship between the canonical diagonal forms and transforming matrices for the two matrices with their canonical diagonal forms and the transforming matrices of their greatest common left divisors and the least common right multiples. The obtained results were used in the ring's stable range calculations.

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Files

aref.doc

dis.pdf

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