A commutative Bezout $PM^{\ast}$ domain is an elementary divisor ring
Algebra and discrete mathematics, Tome 19 (2015) no. 2, pp. 295-301.

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

We prove that any commutative Bezout $PM^{\ast}$ domain is an elementary divisor ring.
Keywords: PM-ring, clean element, neat element, elementary divisor ring, stable range 1, neat range 1.
Mots-clés : Bezout domain
@article{ADM_2015_19_2_a11,
     author = {B. Zabavsky and A. Gatalevych},
     title = {A commutative {Bezout} $PM^{\ast}$ domain is an elementary divisor ring},
     journal = {Algebra and discrete mathematics},
     pages = {295--301},
     publisher = {mathdoc},
     volume = {19},
     number = {2},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2015_19_2_a11/}
}
TY  - JOUR
AU  - B. Zabavsky
AU  - A. Gatalevych
TI  - A commutative Bezout $PM^{\ast}$ domain is an elementary divisor ring
JO  - Algebra and discrete mathematics
PY  - 2015
SP  - 295
EP  - 301
VL  - 19
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ADM_2015_19_2_a11/
LA  - en
ID  - ADM_2015_19_2_a11
ER  - 
%0 Journal Article
%A B. Zabavsky
%A A. Gatalevych
%T A commutative Bezout $PM^{\ast}$ domain is an elementary divisor ring
%J Algebra and discrete mathematics
%D 2015
%P 295-301
%V 19
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ADM_2015_19_2_a11/
%G en
%F ADM_2015_19_2_a11
B. Zabavsky; A. Gatalevych. A commutative Bezout $PM^{\ast}$ domain is an elementary divisor ring. Algebra and discrete mathematics, Tome 19 (2015) no. 2, pp. 295-301. http://geodesic.mathdoc.fr/item/ADM_2015_19_2_a11/

[1] J. W. Brewer, P. F. Conrad, P. R. Montgomery, “Lattice-ordered groups and a conjecture for adequate domains”, Proc. Amer. Math. Soc., 43:1 (1974), 31–34 | DOI | MR

[2] M. Contessa, “On pm-rings”, Comm. Algebra, 10:1 (1982), 93–108 | DOI | MR | Zbl

[3] G. De Marco, A. Orsatti, “Commutative rings in which every prime ideal is contaned in a unigue maximal ideal”, Proc. Amer. Math. Soc., 30:3 (1971), 459–466 | DOI | MR | Zbl

[4] M. Henriksen, “Some remarks about elementary divisor rings”, Michigan Math. J., 3, 1955/56, 159–163 | MR | Zbl

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

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

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

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

[9] W. McGovern, “Neat rings”, J. of Pure and Appl. Algebra, 205:2 (2006), 243–266 | DOI | MR

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

[11] B. V. Zabavsky, “Diagonal reduction of matrices over finite stable range”, Mat. Stud., 41:1 (2014), 101–108 | MR | Zbl

[12] B. V. Zabavsky, “Questions related to the K-theoretical aspect of Bezout rings with various stable range conditions”, Mat. Stud., 42:1 (2014), 89–109 | MR