Noncommutative elementary divisor rings
The main results are the following: Theorem 7. Let R be a Bezout domain and for every finite set \(a_ 1,a_ 2,..\). of non-factorial elements of R there exist an \(a\in R\), such that \(aR=Ra\) and \(a_ i=af_ i\) for a factorial \(f_ i\). Then R is an elementary divisor domain. Theorem 8. Let R be a Bezout domain and for every \(a\in R\) such that \(aR=Ra\), there exists only finitely many maximal elements in the set of all 2-sided ideals lying in aR. Then R is an elementary divisor domain.
scientific article; zbMATH DE number 4045933