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"I liked the algebraic way of looking at things.
I’m additionally fascinated when the algebraic method is applied to infinite objects”.

Irwing Kaplansky

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

 

Bogdan Zabavsky

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 aR a stable range a factor-rings R /aR is not equal 1 then R is not an elementary divisor ring

 

 

 

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Department of Algebra and Logic
Faculty of Mechanics and Mathematics
Ivan Franko National University of L'viv
1 Universytetska Str., 79000 Lviv, Ukraine
Tel: (+380 322) 394 172
E-mail: oromaniv at franko.lviv.ua

Scientific seminar, Aprill, 2015