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On the classification of 3-dimensional coloured Lie algebras

Sergei Silvestrov (1997)

Banach Center Publications

In this paper, complex 3-dimensional Γ-graded ε-skew-symmetric and complex 3-dimensional Γ-graded ε-Lie algebras with either 1-dimensional or zero homogeneous components are classified up to isomorphism.

On the Jacobson radical of graded rings

Andrei V. Kelarev (1992)

Commentationes Mathematicae Universitatis Carolinae

All commutative semigroups S are described such that the Jacobson radical is homogeneous in each ring graded by S .

On the Jacobson radical of strongly group graded rings

Andrei V. Kelarev (1994)

Commentationes Mathematicae Universitatis Carolinae

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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