Abstract
In this paper we study maximal orders over commutative valuation rings in central simple algebras. We are particularly interested in maximal orders which are either Bézout or semihereditary. We construct a class of Bézout maximal orders and a class of semihereditary maximal orders, and show that for any valuation ring V (resp. V with value group Z m ), any Bézout (resp. semihereditary) maximal order over V belongs to the class constructed. Furthermore, we classify all maximal orders in M 2( F) over a valuation ring with value group Z m and in M n ( F) given a mild “defectless” assumption.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
