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Notes on Locally Free Groups
by Chia-Fu Yu

Vol. 12 No. 2 (2017) P.125~P.139
 DOI: https://doi.org/10.21915/BIMAS.2017202 10.21915/BIMAS.2017202

ABSTRACT

A theorem of Swan describes the locally free class group of a maximal order in a central simple algebra over a number field. Swan’s theorem was generalized by Curtis and Reiner to separable algebras for both number fields and global function fields. The proof given by Curtis and Reiner uses Algebraic $K$-Theory. Our motivation is to provide a proof which works for both number fields and global function fields and which does not rely on Algebraic $K$-Theory.

KEYWORDS
ideal class group, lattice, order.

MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: 16H20, 11R52.

MILESTONES