TL;DR
This paper introduces and studies stably free ideal domains, a class of Noetherian and Ore domains where all ideals are stably free, exploring their properties and distinctions.
Contribution
It defines stably free and semi-stably free ideal domains and investigates their algebraic properties and differences from other domain classes.
Findings
Characterization of stably free ideal domains
Properties of semi-stably free ideal domains
Comparison with other Noetherian and Ore domains
Abstract
We define a stably free ideal domain to be a Noetherian domain whose left and right ideals ideals are all stably free. We define also a semi-stably free ideal domain to be an Ore domain whose finitely generated left and right ideals are stably free. Some properties of these rings are studied.
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Taxonomy
TopicsRings, Modules, and Algebras