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