The Noetherian Properties of the Rings of Differential Operators on Central 2-Arrangements

Nakashima, Norihiro

Communications in Algebra, 2013, 41(6), 2114-2131

Permalink : https://hdl.handle.net/2115/55722

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アクセス権	open access
URI	https://hdl.handle.net/2115/55722
タイトル	The Noetherian Properties of the Rings of Differential Operators on Central 2-Arrangements
著者	著者名 Nakashima, Norihiro
言語	英語
キーワード	Hyperplane arrangement
	Noetherian property
	Ring of differential operators
	Primary 13N10
	Secondary 32S22
発行日	2013-05-21
出版者	Taylor & Francis
収録物名	Communications in Algebra
巻(号)	41(6)
ページ	2114-2131
抄録	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.
資源タイプ	学術雑誌論文
出版タイプ	Accepted Manuscript
権利情報	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
PISSN	0092-7872
関連情報 (isVersionOf)	出版社版DOI https://doi.org/10.1080/00927872.2012.654415