The strong Lefschetz property for Artinian algebras with non-standard grading

2007/02/15 by Tadahito Harima, Harima, Tadahito, Junzo Watanabe +1 · 1 citation
Mathematics · #13A99 #13H10 #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC #msc:13A99 #msc:13H10

paper · pdf · doi:10.48550/arxiv.math/0702444

24 pages, To appear in Journal of Algebra

arxiv created 2007/02/15 · arxiv updated 2009/12/01

Abstract

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.

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