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Prime and Primary Ideals in a Prüfer Order in a Simple Artinian Ring with Finite Dimension over its Center |
Canad. Math. Bull. 42(1999), 371-379
Published:1999-09-01
Printed: Sep 1999
Printed: Sep 1999
- H. Marubayashi
- A. Ueda
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 |