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# On Primitive Ideals in Graded Rings

Published:2008-09-01
Printed: Sep 2008
• Agata Smoktunowicz
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## Abstract

Let $R=\bigoplus_{i=1}^{\infty}R_{i}$ be a graded nil ring. It is shown that primitive ideals in $R$ are homogeneous. Let $A=\bigoplus_{i=1}^{\infty}A_{i}$ be a graded non-PI just-infinite dimensional algebra and let $I$ be a prime ideal in $A$. It is shown that either $I=\{0\}$ or $I=A$. Moreover, $A$ is either primitive or Jacobson radical.
 MSC Classifications: 16D60 - Simple and semisimple modules, primitive rings and ideals 16W50 - Graded rings and modules