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On Primitive Ideals in Graded Rings

Published online by Cambridge University Press:  20 November 2018

Agata Smoktunowicz
Agata Smoktunowicz*
Affiliation:
School of Mathematics, University of Edinburgh, Edinburgh EH9 3JZ, Scotland, UK. e-mail: A.Smoktunowicz@ed.ac.uk
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Abstract

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Let $R\,=\,\oplus _{i=1}^{\infty }\,{{R}_{i}}$ be a graded nil ring. It is shown that primitive ideals in $R$ are homogeneous. Let $A\,=\,\oplus _{i=1}^{\infty }\,{{A}_{i}}$ 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.

Keywords

16D6016W50
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 51 , Issue 3 , 01 September 2008 , pp. 460 - 466
Copyright
Copyright © Canadian Mathematical Society 2008

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