Fractionally-semilocal Bezout rings (in Ukrainian)

Author
I. S. Vasiunyk, O. V. Domsha
Ivan Franko National University of Lviv
Abstract
It is proved that a fractionally-semilocal Bezout ring has stable range 3. It is proved that a fractionally-semilocal Bezout ring of stable range 2 is an elementary divisors ring. PM-ring which is a fractionally-semilocal Bezout ring is an elementary divisor ring.
Keywords
fractionally-semilocal rings; stable range
DOI
doi:10.15330/ms.43.2.140-143
Reference
1. Kaplansky I. Elementary divisors and modules// Trans. Amer. Math. Soc. 1949. V.66. P. 464491.

2. Zabavsky B.V. Diagonal reduction of matrices over ring. Mat. Studies, Monograph series, XVI. VNTL: Lviv, 2012. 251 p.

3. Zabavsky B.V. Fractionally regular Bezout ring// Mat. Stud. 2009. V.32, 1. P. 7680.

4. Matlis E. The minimal spectrum of a reduced ring// Illinois J. Math. 1983. V.27, 3. P. 353391.

Pages
140-143
Volume
43
Issue
1
Year
2015
Journal
Matematychni Studii
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