Avoidable rings (in Ukrainian)

Author
B. M. Kuznitska, B. V. Zabavsky
Ivan Franko National University of Lviv
Abstract
In this article we introduce a new class of rings, so called avoidable rings, which are gene- ralizations of adequate rings and neat rings while in these rings every nonzero prime ideal is contained in a unique maximal ideal.
Keywords
avoidable ring; Bezout domain; clean ring; adequate domain
DOI
doi:10.15330/ms.43.2.153-155
Reference
1. Helmer O. The elementary divisor theorem for certain rings without chain condition// Bull. Amer. Math. Soc. 1943. V.49. P. 225236.

2. Kaplansky I. Elementary divisors and modules// Trans. Amer. Math. Soc. 1949. V.66. P. 464491.

3. Gillman L., Henriksen M. Rings of continuous functions in which every finitely generated ideal is principal// Trans. Amer. Math. Soc. 1956. V.82. P. 366391.

4. Gillman L., Henriksen M. Some remarks about elementary divisor rings// Trans. Amer. Math. Soc. 1956. V.82. P. 362365.

5. Larsen M.D., Levis W.J., Shores T. Elementary divisor rings, finitely presented modules// Trans. Amer. Math. Soc. 1974. V.187. P. 231248.

6. Brewer J.W., Conrad P.F., Montgomery P.R. Lattice-ordered groups and a conjecture for adequate domains// Proc. Amer. Math. Soc. 1974. V.43, 1. P. 3135.

7. McGovern W.Wm. Neat rings// J. Pure Appl. Algebra. 2006. V.205. P. 243265.

8. Nicholson W.K. Lifting idempotents and exchange rings// Trans. Amer. Math. Soc. 1977. V.229. P. 269278.

9. Brandal W. Almost maximal integral domains and finitely generated modules// Trans. Amer. Math. Soc. 1973. V.183. P. 203222.

10. Zabavsky B.V. Diagonal reduction of matrices over rings. Mat. Studies, Monograph Series, XVI, VNTL, Lviv, 2012. 251 p.

11. Zabavsky B.V. Diagonal reduction of matrices over finite stable range rings// Mat. Stud. 2014. V.41, 1. P. 101108.

Pages
153-155
Volume
43
Issue
1
Year
2015
Journal
Matematychni Studii
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