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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

Images of Bezout duo-domains

 

 

Olexiy Sorokin

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

 
 

Abstract:

 

We'll generalize some properties of commutative Bezout domains to noncommutative case, especially for quasi-duo and duo-rings. Moreover, we will present the results about square free elements in such rings.

Theorem 1. Right quasi-duo Bezout ring of stable range 1 is an elementary divisor ring iff it is duo-ring.

Theorem 2. Let R be Bezout duo-domain, and a – nonzero element. Then the following conditions are equivalent:

  1.  J(R/aR) is pure ideal;
  2.  a is square free element;
  3.  R/aR is von Neumann regular 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

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