2007年8月
The central simple modules of Artinian Gorenstein algebras
JOURNAL OF PURE AND APPLIED ALGEBRA
- ,
- 巻
- 210
- 号
- 2
- 開始ページ
- 447
- 終了ページ
- 463
- 記述言語
- 英語
- 掲載種別
- DOI
- 10.1016/j.jpaa.2006.10.016
- 出版者・発行元
- ELSEVIER SCIENCE BV
Let A be a standard graded Artinian K-algebra, with char K = 0. We prove the following.
1. A has the Weak Lefschetz Property (resp. Strong Lefschetz Property) if and only if Gr((z)) (A) has the Weak Lefschetz Property (resp. Strong Lefschetz Property) for some linear form z of it. 2. If A is Gorenstein, then A has the Strong Lefschetz Property if and only if there exists a linear form z of A such that all central simple modules of (A, z) have the Strong Lefschetz Property.
As an application of these theorems, we give some new classes of Artinian complete intersections with the Strong Lefschetz Property. (C) 2006 Elsevier B.V. All rights reserved.
1. A has the Weak Lefschetz Property (resp. Strong Lefschetz Property) if and only if Gr((z)) (A) has the Weak Lefschetz Property (resp. Strong Lefschetz Property) for some linear form z of it. 2. If A is Gorenstein, then A has the Strong Lefschetz Property if and only if there exists a linear form z of A such that all central simple modules of (A, z) have the Strong Lefschetz Property.
As an application of these theorems, we give some new classes of Artinian complete intersections with the Strong Lefschetz Property. (C) 2006 Elsevier B.V. All rights reserved.
- リンク情報
- ID情報
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- DOI : 10.1016/j.jpaa.2006.10.016
- ISSN : 0022-4049
- Web of Science ID : WOS:000246641200010