Abstract
We investigate the structure of matrices and their divisors over the domain of principal ideals.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
V. M. Prokip, “On multiplicativity of canonical diagonal forms for matrices over the domain of principal ideals,” Ukr. Mat. Zh., 53, No. 2, 274–277 (2001).
M. Newman, Integral Matrices, Academic Press, New York (1972).
B. V. Zabavskii and P. S. Kazimirskii, “Reduction of a pair of matrices over an adequate ring to a special triangular form by identical one-sided transformations,” Ukr. Mat. Zh., 36, No. 2, 256–258 (1984).
V. Petrychkovych, “Generalized equivalence of pairs of matrices,” Lin. Multilin. Algebra, 48, 179–188 (2000).
O. Helmer, “The elementary divisors for certain rings without chain condition,” Bull. Amer. Math. Soc., 49, 225–236 (1943).
V.M. Prokip, “On multiplicativity of canonical diagonal forms of matrices,” Izv. Vyssh. Uchebn. Zaved., Ser. Mat., No. 7, 60–62 (1992).
W. H. Gustafson, “Roth's theorem over commutative rings,” Lin. Algebra Appl., 23, 245–251 (1979).
P. S. Kazimirs'kyi, Factorization of Matrix Polynomials [in Ukrainian], Naukova Dumka, Kiev (1982).
V. M. Prokip, “On divisibility of one-sided equivalence of polynomial matrices,” Ukr. Mat. Zh., 42, No. 9, 1213–1219 (1990).
M. D. Larsen, W. J. Lewis, and T. S. Shores, “Elementary divisors rings and finitely presented modules,” Trans. Amer. Math. Soc., 187, No. 1, 231–248 (1974).
V. P. Shchedryk, “Structure and properties of divisors of matrices over a commutative domain of elementary divisors,” Mat. Stud., 10, No. 2, 115–120 (1998).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Prokip, V.M. Structure of Matrices and Their Divisors over the Domain of Principal Ideals. Ukrainian Mathematical Journal 54, 1378–1385 (2002). https://doi.org/10.1023/A:1023491809453
Issue Date:
DOI: https://doi.org/10.1023/A:1023491809453