Unique maximal Betti diagrams for Artinian Gorenstein k-algebras with the weak Lefschetz property

被引：0

作者：

Richert, Ben ^{[1
]}

机构：

[1] Calif Polytech State Univ San Luis Obispo, Dept Math, San Luis Obispo, CA 93407 USA

来源：

COMMUNICATIONS IN ALGEBRA | 2024年 / 52卷 / 06期

关键词：

Artinian Gorenstein k-algebras; Graded Betti numbers; Hilbert functions; NUMBERS;

D O I：

10.1080/00927872.2023.2301515

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We give an alternate proof for a theorem of Migliore and Nagel. In particular, we show that if H is an SI-sequence, then the collection of Betti diagrams for all Artinian Gorenstein k-algebras with the weak Lefschetz property and Hilbert function H has a unique largest element.

引用

页码：2368 / 2385

页数：18

共 33 条

[1] On the Weak-Lefschetz property for Artinian Gorenstein algebras
Ragusa A.
Zappalà G.
Rendiconti del Circolo Matematico di Palermo, 2013, 62 (2) : 199 - 206
[2] The Weak and Strong Lefschetz properties for Artinian K-algebras
Harima, T
Migliore, JC
Nagel, U
Watanabe, J
JOURNAL OF ALGEBRA, 2003, 262 (01) : 99 - 126
[3] On the Weak Lefschetz Property for artinian Gorenstein algebras of codimension three
Boij, Mats
Migliore, Juan
Miro-Roig, Rosa M.
Nagel, Uwe
Zanello, Fabrizio
JOURNAL OF ALGEBRA, 2014, 403 : 48 - 68
[4] The weak Lefschetz property for Artinian Gorenstein algebras of codimension three
Miro-Roig, Rosa M.
Quang Hoa Tran
JOURNAL OF PURE AND APPLIED ALGEBRA, 2020, 224 (07)
[5] The finite free extension of Artinian K-algebras with the strong Lefschetz property.
Harima, T
Watanabe, J
RENDICONTI DEL SEMINARIO MATEMATICO DELLA UNIVERSITA DI PADOVA, 2003, 110 : 119 - 146
[6] HILBERT FUNCTIONS OF ARTINIAN GORENSTEIN ALGEBRAS WITH THE STRONG LEFSCHETZ PROPERTY
Altafi, Nasrin
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2022, 150 (02) : 499 - 513
[7] The Weak Lefschetz Property of Artinian Algebras Associated to Paths and Cycles
Nguyen, Hop D.
Tran, Quang Hoa
ACTA MATHEMATICA VIETNAMICA, 2024, 49 (03) : 523 - 544
[8] The weak Lefschetz property for Standard graded, Artinian Gorenstein algebras of embedding dimension four and socle degree three
Kustin, Andrew R.
JOURNAL OF ALGEBRA, 2024, 650 : 80 - 122
[9] LEFSCHETZ PROPERTIES FOR ARTINIAN GORENSTEIN ALGEBRAS PRESENTED BY QUADRICS
Gondim, Rodrigo
Zappala, Giuseppe
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2018, 146 (03) : 993 - 1003
[10] BETTI NUMBERS FOR CONNECTED SUMS OF GRADED GORENSTEIN ARTINIAN ALGEBRAS
Altafi, Nasrin
Di Gennaro, Roberta
Galetto, Federico
Grate, Sean
Miro-Roig, Rosa M.
Nagel, Uwe
Seceleanu, Alexandra
Watanabe, Junzo
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2025, 378 (02) : 1055 - 1080

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