This article is cited in 6 papers

RESEARCH ARTICLE

Factorization of matrices over elementary divisor domain

Volodymyr Shchedryk

Pidstryhach Institute for Applied Problems of Mechanics and Mathematics NAS of Ukraine,3b Naukova Str., L'viv, 79053, Ukraine

Abstract: We propose constructive criteria of divisibility and associativity of matrices over commutative elementary divisor ring without zero divisors. On this base, the explicit form for all non-associated divisors which have prescribed canonical diagonal forms (c.d.f.) is indicated. A relation between c.d.f. for matrix and c.d.f. for its divisors is established. The uniqueness theorem is proved.

Keywords: elementary divisor ring, canonical diagonal form, factorization of matrices up to associate, divisor of matrices.

MSC: 15A21

Received: 01.03.2006
Revised: 15.05.2009

Language: English

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