Abstract
We introduce a new class of rings of elementary divisors which generalize adequate rings. We show that the problem of whether every commutative Bezout domain is a domain of elementary divisors reduces to the case where the domain contains only trivial adequate elements (namely, the identities of the domain).
References
O. Helmer, “The elementary divisor theorem for certain rings without chain conditions,” Bull. Amer. Math. Soc., 49, 225–236 (1974).
M. Henriksen, “Some remarks about elementary divisor rings,” Michigan Math. J., 3, 159–163 (1955/1956).
I. Kaplansky, “Elementary divisors and modules,” Trans. Amer. Math. Soc., 66, 464–491 (1949).
B. V. Zabavskii and M. Ya. Komarnitskii, “On adequate rings,” Visn. L’viv. Univ., Issue 30, 39–43 (1988).
N. D. Larsen, W. I. Lewin, and T. S. Shores, “Elementary divisor rings and finitely presented modules,” T rans. Amer. Math. Soc., 187, 231–248 (1974).
I. Gillman and M. Henriksen, “Some remarks about elementary divisor rings,” Trans. Amer. Math. Soc., 82, 362–365 (1956).
M. Ya. Komarnitskii and B. V. Zabavskii, “On the adequacy of one class of Bezout domains,” in: Abstracts of the 19th All-Union Algebraic Conference, Vol. 1, Lvov (1977), p. 160.
Rights and permissions
About this article
Cite this article
Zabavskii, B.V. Generalized adequate rings. Ukr Math J 48, 614–617 (1996). https://doi.org/10.1007/BF02390621
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02390621