Geodesic
A criterion of elementary divisor domain for distributive domains
Algebra and discrete mathematics, Tome 23 (2017) no. 1, pp. 1-6 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this paper we introduce the notion of the neat range one for Bezout duo-domains. We show that a distributive Bezout domain is an elementary divisor domain if and only if it is a duo-domain of neat range one.
Keywords: neat ring, clear ring, elementary divisor ring, stable range one, neat range one.
Mots-clés : distributive domain, Bezout duo-domain 
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V. Bokhonko; B. Zabavsky. A criterion of elementary divisor domain for distributive domains. Algebra and discrete mathematics, Tome 23 (2017) no. 1, pp. 1-6. http://geodesic.mathdoc.fr/item/ADM_2017_23_1_a1/

[1] Kaplansky I., “Elementary divisirs and modules”, Trans. Amer. Math. Soc., 66 (1949), 464–491 | DOI | MR | Zbl

[2] Nicholson W. K., “Lifting idempotents and exchange rings”, Trans. Amer. Math. Soc., 229 (1977), 269–278 | DOI | MR | Zbl

[3] Tuganbaev A. A., “Rings of elementary divisors and distributive rings”, Russian. Math. Surveys, 46:6 (1991), 219–220 | DOI | MR

[4] Zabavsky B. V., Diagonal reduction of matrices over rings, Mathematical Studies, Monograph Series, XVI, Lviv, 2012, 251 pp. | MR | Zbl

[5] Zabavsky B. V., Komarnytskii M. Y., “Distributive elementary divisor domain”, Ukr. Mat. J., 42:7 (1990), 1000–1004 | MR