# Lefschetz Properties

• Toshiaki Maeno
• Hideaki Morita
• Yasuhide Numata
• Akihito Wachi
• Junzo Watanabe
Chapter
Part of the Lecture Notes in Mathematics book series (LNM, volume 2080)

## Abstract

Let $$A =\bigoplus _{ i=0}^{c}A_{i},$$ A c ≠ 0, be a graded Artinian algebra. We say that A has the weak Lefschetz property (WLP) if there exists an element LA 1 such that the multiplication map
$$\displaystyle\begin{array}{rcl} \times L: A_{i} \rightarrow A_{i+1}& & {}\\ \end{array}$$
has full rank for all 0 ≤ ic − 1. We call LA 1 with this property a weak Lefschetz element.

## Keywords

Irreducible Component Complete Intersection Hilbert Series Hilbert Function Jordan Block
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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## Authors and Affiliations

• 1
• Toshiaki Maeno
• 2
• Hideaki Morita
• 3
• Yasuhide Numata
• 4
• Akihito Wachi
• 5
• Junzo Watanabe
• 6
1. 1.Department of Mathematics EducationNiigata UniversityNiigataJapan
2. 2.Department of MathematicsMeijo UniversityNagoyaJapan
3. 3.Muroran Institute of TechnologyMuroranJapan
4. 4.Department of Mathematical SciencesShinshu UniversityMatsumotoJapan
5. 5.Department of MathematicsHokkaido University of EducationKushiroJapan
6. 6.Department of MathematicsTokai UniversityHiratsukaJapan