A Note on the Jacobson Radical of a Graded Ring
DOI:
https://doi.org/10.5644/SJM.11.2.03Keywords:
Graded rings and modules, regular anneids and moduloids, Jacobson radicalAbstract
We prove that $J(R_e)=R_e\cap J(R),$ where $S$ is a cancellative partial groupoid with idempotent $e,$ $R=\bigoplus_{s\in S}R_s$ an Artinian $S$-graded ring inducing $S,$ $J(R)$ the Jacobson radical of $R$ and $J(R_e)$ the Jacobson radical of $R_e.$ We also prove that $J(R)$ is nil if $J(R_e)$ is nil under certain assumptions.
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