Comaximal factorization in a commutative Bezout ring
Algebra and discrete mathematics, Tome 30 (2020) no. 1, pp. 150-160.

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

We study an analogue of unique factorization rings in the case of an elementary divisor domain.
Keywords: Bezout ring, clean ring, neat ring, elementary divisor ring, stable range one, stable range two, neat range one, pseudo-irreducible element.
@article{ADM_2020_30_1_a11,
     author = {B. Zabavsky and O. Romaniv and B. Kuznitska and T. Hlova},
     title = {Comaximal factorization in a commutative {Bezout} ring},
     journal = {Algebra and discrete mathematics},
     pages = {150--160},
     publisher = {mathdoc},
     volume = {30},
     number = {1},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2020_30_1_a11/}
}
TY  - JOUR
AU  - B. Zabavsky
AU  - O. Romaniv
AU  - B. Kuznitska
AU  - T. Hlova
TI  - Comaximal factorization in a commutative Bezout ring
JO  - Algebra and discrete mathematics
PY  - 2020
SP  - 150
EP  - 160
VL  - 30
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ADM_2020_30_1_a11/
LA  - en
ID  - ADM_2020_30_1_a11
ER  - 
%0 Journal Article
%A B. Zabavsky
%A O. Romaniv
%A B. Kuznitska
%A T. Hlova
%T Comaximal factorization in a commutative Bezout ring
%J Algebra and discrete mathematics
%D 2020
%P 150-160
%V 30
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ADM_2020_30_1_a11/
%G en
%F ADM_2020_30_1_a11
B. Zabavsky; O. Romaniv; B. Kuznitska; T. Hlova. Comaximal factorization in a commutative Bezout ring. Algebra and discrete mathematics, Tome 30 (2020) no. 1, pp. 150-160. http://geodesic.mathdoc.fr/item/ADM_2020_30_1_a11/

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

[2] J. H. M. Wedderburn “On matrices whose coefficients are functions of single variable”, Trans. Amer. Math. Soc., 16:2 (1915), 328–332 | MR | Zbl

[3] O. Helmer, “The elementary divisor theorem for certain rings without chain conditions”, Bull. Amer. Math. Soc., 49:2 (1943), 225–236 | DOI | MR | Zbl

[4] M. Henriksen, “Some remarks about elementary divsor rings”, Michigan Math. J., 3 (1955-1956), 159–163 | DOI | MR

[5] B. V. Zabavsky, Diagonal reduction of matrices over rings, Mathematical Studies, XVI, VNTL Publishers, Lviv, 2012 | MR | Zbl

[6] B. V. Zabavsky, “Diagonal reduction of matrices over finite stable range rings”, Mat. Stud., 41 (2014), 101–108 | MR | Zbl

[7] W. Wm. McGovern, “Neat ring”, J. Pure and Appl. Algebra, 205 (2006), 243–265 | DOI | MR | Zbl

[8] J. W. Brewer, W. J. Heinzer, “On decomposing ideals in to product of comaximal ideals”, Commun. Algebra, 30 (2002), 5999–6010 | DOI | MR | Zbl

[9] M. D. Larsen, W. J. Lewis, T. S. Shores, “Elementary divisor rings and finitely presented modules”, Trans. Amer. Math. Soc., 187 (1974), 231–248 | DOI | MR | Zbl

[10] R. Gordon, J. C. Robson, Krull Dimension, Memoirs of the American Mathematical Society, 133, American Mathematical Society, Providence, R.I., 1973, ii+78 pp. | MR | Zbl

[11] B. V. Zabavsky, “Fractionally regular Bezout rings”, Matem. Stud., 32:1 (2009), 76–80 | MR | Zbl