A~criterion of elementary divisor domain for distributive domains
Algebra and discrete mathematics, Tome 23 (2017) no. 1, pp. 1-6.

Voir la notice de l'article provenant de la source Math-Net.Ru

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
@article{ADM_2017_23_1_a1,
     author = {V. Bokhonko and B. Zabavsky},
     title = {A~criterion of elementary divisor domain for distributive domains},
     journal = {Algebra and discrete mathematics},
     pages = {1--6},
     publisher = {mathdoc},
     volume = {23},
     number = {1},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2017_23_1_a1/}
}
TY  - JOUR
AU  - V. Bokhonko
AU  - B. Zabavsky
TI  - A~criterion of elementary divisor domain for distributive domains
JO  - Algebra and discrete mathematics
PY  - 2017
SP  - 1
EP  - 6
VL  - 23
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ADM_2017_23_1_a1/
LA  - en
ID  - ADM_2017_23_1_a1
ER  - 
%0 Journal Article
%A V. Bokhonko
%A B. Zabavsky
%T A~criterion of elementary divisor domain for distributive domains
%J Algebra and discrete mathematics
%D 2017
%P 1-6
%V 23
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ADM_2017_23_1_a1/
%G en
%F ADM_2017_23_1_a1
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