Homogeneity of the radical of semigroup-graded rings

摘要

We show that cancellativity is a necessary condition on a semigroupSfor the Jacobson radical of allS-graded rings to be homogeneous. We introduce some related classes of semigroupsSfor which the Jacobson radical of certainS-graded rings is always homogeneous. Commutative and regular semigroups in these classes are described