# The connection of the prime spectrum geometry of a commutative Bezout domain and its stable range

- Written by B. Zabavsky
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Professor

Department of Algebra and Logic

Faculty of Mechanics and Mathematics

Ivan Franko National University of L'viv

Abstract:

*It will be shown how the prime spectrum geometry of a commutative Bezout domain influences on its stable range in whats cases the stable range of a commutative Bezout domain becomes equal 1*

**Theоrem**. *Let R be a commutative Bezout domain. If for each nonzero element a∈R a stable range a factor-rings R /aR is not equal 1 then R is not an elementary divisor ring*

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