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The Noetherian Properties of the Rings of Differential Operators on Central 2-Arrangements
| Title: | The Noetherian Properties of the Rings of Differential Operators on Central 2-Arrangements |
| Authors: | Nakashima, Norihiro Browse this author |
| Keywords: | Hyperplane arrangement | | Noetherian property | | Ring of differential operators | | Primary 13N10 | | Secondary 32S22 |
| Issue Date: | 21-May-2013 |
| Publisher: | Taylor & Francis |
| Journal Title: | Communications in Algebra |
| Volume: | 41 |
| Issue: | 6 |
| Start Page: | 2114 |
| End Page: | 2131 |
| Publisher DOI: | 10.1080/00927872.2012.654415 |
| Abstract: | Whereas Holm proved that the ring of differential operators on a generic hyperplane arrangement is finitely generated as an algebra, the problem of its Noetherian properties is still open. In this article, after proving that the ring of differential operators on a central arrangement is right Noetherian if and only if it is left Noetherian, we prove that the ring of differential operators on a central 2-arrangement is Noetherian. In addition, we prove that its graded ring associated to the order filtration is not Noetherian when the number of the consistuent hyperplanes is greater than 1. |
| Rights: | This is an Accepted Manuscript of an article published by Communications in Algebra, 41(6) May 2013, 2114-2131. Communications in Algebra is available online at: http://www.tandfonline.com/doi/full/10.1080/00927872.2012.654415#.UjEZ0D-ub3g |
| Type: | article (author version) |
| URI: | http://hdl.handle.net/2115/55722 |
| Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)
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Submitter: 中島 規博
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