All commutative semigroups $S$ are described such that the Jacobson radical is homogeneous in each ring graded by $S$.
@article{118465, author = {Andrei V. Kelarev}, title = {On the Jacobson radical of graded rings}, journal = {Commentationes Mathematicae Universitatis Carolinae}, volume = {33}, year = {1992}, pages = {21-24}, zbl = {0815.16025}, mrnumber = {1173741}, language = {en}, url = {http://dml.mathdoc.fr/item/118465} }
Kelarev, Andrei V. On the Jacobson radical of graded rings. Commentationes Mathematicae Universitatis Carolinae, Tome 33 (1992) pp. 21-24. http://gdmltest.u-ga.fr/item/118465/
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