On a theorem of Cohen and Montgomery for graded rings
Published online by Cambridge University Press: 12 July 2007
Abstract
Giving as answer to Bergman's question, Cohen and Montgomery proved that, for every finite group G with identity e and each G-graded ring R = ⊕g∈GRg, the Jacobson radical J(Re) of the initial component Re is equal to Re ∩ J(R). We describe all semigroups S, which satisfy the following natural analogue of this property: J(Re) = Re ∩ J(R) for each S-graded ring R = ⊕s∈SRs and every idempotent e ∈ S.
- Type
- Research Article
- Information
- Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 131 , Issue 5 , October 2001 , pp. 1163 - 1166
- Copyright
- Copyright © Royal Society of Edinburgh 2001
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