Abstract
In this note definitions of the Jacobson radical of 2-graded rings are given which are analogous to the usual definitions for associative rings in terms of maximal modular one-sided ideals and of primitive ideals. We show that these definitions lead to the same ideal and are left-right symmetric. The relationship between the Jacobson radical of the 2-graded ring and that of the associated associative ring is also investigated. Preliminaries
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