On Primitive Ideals in Graded Rings

http://dx.doi.org/10.4153/CMB-2008-046-1
Canad. Math. Bull. 51(2008), 460-466

  Published:2008-09-01
 Printed: Sep 2008

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.