Menu

"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.

 

 

  • Коментарі не знайдено

Залиште свій коментар

Post comment as a guest

0
back to top
Bookmaker with best odds http://wbetting.co.uk review site.
Divertissement

Адміністратор, 16 Sep, 2016

Divertissement

On some open Zabavsky’s problems

A. Romaniv, 15 Mar, 2013

On some open Zabavsky’s problems

links

links

contacts us

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, August, 2017