Applications of epigroups to graded ring theory.

A.V. Kelarev

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Andrei V. Kelarev (1994)

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For any non-torsion group $G$ with identity $e$ , we construct a strongly $G$ -graded ring $R$ such that the Jacobson radical $J (R_{e})$ is locally nilpotent, but $J (R)$ is not locally nilpotent. This answers a question posed by Puczyłowski.

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We study the weak dimension of a group-graded ring using methods developed in [B1], [Q] and [R]. We prove that if R is a G-graded ring with G locally finite and the order of every subgroup of G is invertible in R, then the graded weak dimension of R is equal to the ungraded one.

Superlinear algebra or two-graded algebraic structures.

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