On the upper nilradical and Jacobson radical of rings graded by t.u.p.-semigroups

@inproceedings{Madill2015OnTU,
  title={On the upper nilradical and Jacobson radical of rings graded by t.u.p.-semigroups},
  author={Blake Madill},
  year={2015}
}
Given a t.u.p.-semigroup (two unique product semigroup) $X$, we show if $R$ is an $X$-graded ring then both its nilradical and Jacobson radical are homogeneous. This partially answers questions of Smoktunowicz and Jespers. 

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