Showing papers by "Andrei V. Kelarev published in 1996"
5 citations
TL;DR: The question of whether the Jacobson radical of a ring is semiprimitive has been studied in the context of semigroup groups as mentioned in this paper, where the assumption that the radical is homogeneous in every algebra of characteristic zero has been shown to be false.
4 citations
01 Jan 1996
TL;DR: In this paper, it was shown that the Jacobson radical is homogeneous in every algebra graded by a linear cancellative semigroup, and that the semigroup algebra of every linear cancellation semigroup is semisimple.
Abstract: We consider algebras over a field of characteristic zero, and prove that the Jacobson radical is homogeneous in every algebra graded by a linear cancellative semigroup. It follows that the semigroup algebra of every linear cancellative semigroup is semisimple. © 1996 American Mathematical Society.
3 citations
TL;DR: In this paper, a new class of semigroups S including all locally finite, completely regular and strongly π-regular linear semiigroups is introduced and the structure of the Jacobson radical of R is reduced to the radicals of subrings graded by the maximal subgroups of S. In two special cases the reduction is simplified.
Abstract: We introduce a new large class of semigroups S including all locally finite, completely regular and strongly π-regular linear semigroups. For any semigroup S in the class and any S-graded ring R, the structure of the Jacobson radical of R is reduced to the radicals of subrings graded by the maximal subgroups of S. Many results on radicals follow from this reduction in a unified way. In two special cases the reduction is simplified.
1 citations
TL;DR: In this paper, the authors give necessary and sufficient conditions on the semigroup S for the Jacobson radical to be S-invariant, and show that S is a semigroup with sufficient conditions.
Abstract: We give necessary and sufficient conditions on the semigroup S for the Jacobson radical to be S-invariant.