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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

Commutativity theorem and distributive rings of stable range 1

 

 

Andry Gatalevych

Associate Professor
Department of Algebra and Logic
Faculty of Mechanics and Mathematics
Ivan Franko National University of L'viv

 
 

Abstract:

 

Theоrem 1.
A unit-central simple Bezout domain  R  with stable range 1 is an elementary divisor ring iff  is a field.

Theоrem 2.
Let  R  be a ring with stable range 1. Then from the condition  aR+bR=R it follows there exist element  u∈ U(R)  that   Ra+Rbu=R.

Theоrem 3.
A unit-central Bezout ring  with stable range 1 is an elementary divisor ring iff  R  is a duo-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, May, 2018