32 research outputs found
The strong Lefschetz property for Artinian algebras with non-standard grading
We define the strong Lefschetz property for finite graded modules over graded
Artinian algebras whose grading is not necessarily standard. We show that most
results which have been obtained for Artinian algebras with standard grading
can be extended for non-standard grading. Our results on the strong Lefschetz
property for non-standard grading can be used to prove that certain Artinian
complete intersections with standard grading have the strong Lefschetz
property.Comment: 24 pages, To appear in Journal of Algebr
A note on Artinian Gorenstein algebras of codimension three
AbstractIn this paper, using a standard fact in linkage theory, we give a new construction of Artinian Gorenstein algebras achieving all possible sets of graded Betti numbers for codimension three. Furthermore, as an application, we give another proof of Stanley's well-known characterization theorem for the Hilbert functions of codimension three Artinian Gorenstein algebras