Department of Algebra and Logic
Faculty of Mechanics and Mathematics
Ivan Franko National University of L'viv
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:
- J(R/aR) is pure ideal;
- a is square free element;
- R/aR is von Neumann regular ring
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