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On Primitive Ideals in Graded Rings
Published online by Cambridge University Press: 20 November 2018
Abstract
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.
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- Copyright © Canadian Mathematical Society 2008
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