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# Non-Isomorphic Maximal Orders with Isomorphic Matrix Rings

Published:2000-12-01
Printed: Dec 2000
• A. W. Chatters
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## Abstract

We construct a countably infinite family of pairwise non-isomorphic maximal ${\mathbb Q}[X]$-orders such that the full $2$ by $2$ matrix rings over these orders are all isomorphic.
 MSC Classifications: 16S50 - Endomorphism rings; matrix rings [See also 15-XX] 16H05 - Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.) 16N60 - Prime and semiprime rings [See also 16D60, 16U10]