arXiv subjects

Bogdan Zabavsky

Publications and source records attributed to Bogdan Zabavsky.

2 recordsLinked to original sources

arXiv2015

Conditions for stable range of an elementary divisor rings

Using the concept of ring of Gelfand range 1 we proved that a commutative Bezout domain is an elementary divisor ring iff it is a ring of Gelfand range 1. Obtained results give a solution of problem of elementary divisor rings for different classes of commutative Bezout domains, in particular, $PM^{*}$, local Gelfand domains and so on.

math.RA↗

arXiv2012

A commutative Bezout domain in which every maximal ideal is principal is an elementary divisor ring

In this article we revisit a problem regarding Bezout domains, namely, whether every Bezout domain is an elementary divisor domain. We prove that a Bezout domain in which every maximal ideal is principal is an elementary divisor ring

math.RA↗