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Homogeneity of the radical of semigroup-graded rings |
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| Authors: | MV Clase AV Kelarev |
| Institution: | 1. Department of Mathematics and Statistics , Memorial University of Newfoundland St.John's , Newfoundland, A1C 5S7, Canada E-mail: mclass@albert.math.mun.ca;2. Department of Mathematics , University of Stellenbosch , Stellenbosch, 7600, South africa E-mail: avk@maties.sun.ac.za |
| Abstract: | We show that cancellativity is a necessary condition on a semigroup S for the Jacobson radical of all S-graded rings to be homogeneous. We introduce some related classes of semigroups S for which the Jacobson radical of certain S-graded rings is always homogeneous. Commutative and regular semigroups in these classes are described |
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