On a theorem of Cohen and Montgomery for graded rings

Author： Kelarev A. V.  

Publisher： Royal Society of Edinburgh

ISSN： 1473-7124

Source： Proceedings Section A: Mathematics - Royal Society of Edinburgh, Vol.131, Iss.5, 2001-10, pp. : 1163-1166

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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.

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