Year: 2026
Type: preprint
Abstract: We settle in the negative the longstanding question whether every Bézout domain is an elementary divisor domain by constructing a Bézout domain over which an explicit $2\times 2$ matrix has no Smith normal form. The obstruction is topological and is detected by the Möbius line bundle.
Source: arXiv (Cornell University)
Authors: Hägg, Christian, Mörtberg, Anders
Language: English
Topic: Rings, Modules, and Algebras
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214796105