The central simple modules of Artinian Gorenstein algebras

Details The central simple modules of Artinian Gorenstein algebras The central simple modules of Artinian Gorenstein algebras

2006-12-13

arxiv.org/abs/math/0612344v1

Mathematics

Commutative Algebra

20 pages, To be published in Journal of Pure and Applied Algebra

Scientific paper

Let A be a standard graded Artinian algebra over a field of characteristic zero and let z be a linear form in A. We define the central simple modules for each such pair (A, z). Assume that A is Gorenstein. Then we prove that A has the strong Lefschetz property if and only if there exists a linear form z in A such that all central simple modules of the pair (A,z) have the strong Lefschetz property. In the course of proof we need to extend the definition of the strong Lefschetz property to finite graded modules over graded Artinian algebra, which previously was defined only for standard graded Artinian algebras.

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