Elementary divisor domains and Bézout domains
Every elementary divisor domain is a Bézout domain; whether the converse holds is still an open question which dates as far back as 1942, (see \textit{O. Helmer} [Bull. Am. Math. Soc. 49, 225--236 (1943; Zbl 0060.07606)]). The paper under review addresses two issues. Firstly, it provides several hitherto unknown implications between an elementary divisor domain and a Bézout domain. Secondly, by starting with a commutative ring \(R\) which is not necessarily Bézout, the author constructs new Bézout rings associated with \(R\). In the methods employed, symmetric matrices, matrices with trace zero and linear homogeneous polynomials play a crucial role.
scientific article; zbMATH DE number 6166678
scientific article