Geodesic
Factorization of matrices over elementary divisor domain
Algebra and discrete mathematics, no. 2 (2009), pp. 79-98

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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. 
@article{ADM_2009_2_a6,
     author = {Volodymyr Shchedryk},
     title = {Factorization of  matrices over elementary divisor domain},
     journal = {Algebra and discrete mathematics},
     pages = {79--98},
     publisher = {mathdoc},
     number = {2},
     year = {2009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2009_2_a6/}
}
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Volodymyr Shchedryk. Factorization of  matrices over elementary divisor domain. Algebra and discrete mathematics, no. 2 (2009), pp. 79-98. http://geodesic.mathdoc.fr/item/ADM_2009_2_a6/