Bounded elementary divisor domains of stable range 1

S.I.Bilavska

It is proved that any restricted Bezout domain of stable rank 1 in which the Dubrovin condition is satisfied and where a maximal non principal left ideal is an elementary divisor domain.

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7. Beauregard R. Left Ore principal right ideal domains// Proc. Amer. Math.Soc. -- 1988. -- V.102, No.3. -- P. 459--462.

8. Kaplansky I. Elementary divisors and modules// Trans. Amer. Math.Soc. -- 1949. -- V.66. -- P. 469--491.

9. Zabavsky B.V., Gatalevich A.I. Maximal non-principal right ideals Bezout domain// Math. Method and phiz.-math. field. -- 2000. -- V.43, No.2. -- P. 40--44. (in Ukrainian)

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	Bounded elementary divisor domains of stable range 1
Author	S.I.Bilavska Ivan Franko National University of Lviv, Department of Mechanics and Mathematics
Abstract	It is proved that any restricted Bezout domain of stable rank 1 in which the Dubrovin condition is satisfied and where a maximal non principal left ideal is an elementary divisor domain.
Keywords	restricted Bezout domain, Dubrovin condition, elementary divisor domain, stable rank
DOI	doi:10.30970/ms.34.1.44-47
Reference	1. Zabavsky B.V. About non-commutative rings elementary divisor// Ukr. Math. J. -- 1987. -- V.39. -- P.~440--444. (in Ukrainian) 2. Beauregard R.A. Infinite primes and unique factorization in a principal right ideal domain// Trans. Amer. Math. Soc. -- 1969. -- V.44. -- P. 245--254. 3. Zabavsky B.V. Diagonalizabilyty theorems for rings with finite stable range// Alg. and Discrete Math. -- 2004. -- V.2. -- P. 84--90. 4. Dubrovin N.I. About elementary divisor rings// Izvestia vuzov Mathematica. -- 1986. -- V.11. -- P. 14--20.(in Russian) 5. Zabavsky B.V. Almost atom elementary divisor domains of stable range 1// Mat. Stud. -- 2006. -- V.26, No.2. -- P. 212--216. (in Ukrainian) 6. Cohn P.M. Right principal Bezout domains// J.London Math. Soc. -- 1987. -- V.35, No.2. -- P. 251--262. 7. Beauregard R. Left Ore principal right ideal domains// Proc. Amer. Math.Soc. -- 1988. -- V.102, No.3. -- P. 459--462. 8. Kaplansky I. Elementary divisors and modules// Trans. Amer. Math.Soc. -- 1949. -- V.66. -- P. 469--491. 9. Zabavsky B.V., Gatalevich A.I. Maximal non-principal right ideals Bezout domain// Math. Method and phiz.-math. field. -- 2000. -- V.43, No.2. -- P. 40--44. (in Ukrainian) 10. Cohn P.M. Free rings and their relations. -- Acad. Press. London. New York, 1971.
Pages	44-47
Volume	34
Issue	1
Year	2010
Journal	Matematychni Studii
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