Finitely Presented Monoids and Algebras defined by Permutation Relations of Abelian Type

الأصل · EN

The class of finitely presented algebras over a field K with a set of generators a₁,...,aₙ and defined by homogeneous relations of the form a₁a₂...aₙ = asigma(1)asigma(2)...asigma(n), where sigma runs through an abelian subgroup H of Symₙ, the symmetric group, is considered. It is proved that the Jacobson radical of such algebras is zero. Also, it is characterized when the monoid Sₙ(H), with the "same" presentation as the algebra, is cancellative in terms of the stabilizer of 1 and the stabilizer of n in H. This work is a continuation of earlier work of Cedo, Jespers and Okninski.