The strong Lefschetz property of certain modules over Clements-Lindström rings
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866913401826967552 |
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| author | Chase, Bek |
| author_facet | Chase, Bek |
| contents | We introduce a method for studying the Lefschetz properties for $k[x,y]$-modules based on the Lindström-Gessel-Viennot Lemma. In particular, we prove that certain modules over Artinian Clements-Lindström rings in characteristic zero have the strong Lefschetz property. In particular, we show that every homogeneous idea in a Clements-Lindström ring of embedding dimension two has the strong Lefschetz property. As an application, we study the strong Lefschetz property of type two monomial ideals of codimension three. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_15919 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The strong Lefschetz property of certain modules over Clements-Lindström rings Chase, Bek Commutative Algebra We introduce a method for studying the Lefschetz properties for $k[x,y]$-modules based on the Lindström-Gessel-Viennot Lemma. In particular, we prove that certain modules over Artinian Clements-Lindström rings in characteristic zero have the strong Lefschetz property. In particular, we show that every homogeneous idea in a Clements-Lindström ring of embedding dimension two has the strong Lefschetz property. As an application, we study the strong Lefschetz property of type two monomial ideals of codimension three. |
| title | The strong Lefschetz property of certain modules over Clements-Lindström rings |
| topic | Commutative Algebra |
| url | https://arxiv.org/abs/2406.15919 |