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# Prime and Primary Ideals in a Prüfer Order in a Simple Artinian Ring with Finite Dimension over its Center

Published:1999-09-01
Printed: Sep 1999
• H. Marubayashi
• A. Ueda
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## Abstract

Let $Q$ be a simple Artinian ring with finite dimension over its center. An order $R$ in $Q$ is said to be {\it Pr\"ufer\/} if any one-sided $R$-ideal is a progenerator. We study prime and primary ideals of a Pr\"ufer order under the condition that the center is Pr\"ufer. Also we characterize branched and unbranched prime ideals of a Pr\"ufer order.
 MSC Classifications: 16H05 - Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.) 16L30 - Noncommutative local and semilocal rings, perfect rings

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