关于强Lefschetz性质的Stanley定理的一个新证明

IF 0.4 4区数学 Q4 MATHEMATICS

Colloquium Mathematicum Pub Date : 2022-11-24 DOI:10.4064/cm8987-11-2022

Hong Phuong, Quang Hoa Tran

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引用次数: 2

摘要

.由于Stanley在1980年提出的一个标准分次artinian单体完全交代数A=k[x1，x2，…，xn]/（x1，x2 2，…，xan n），其特征域为零，具有强Lefschetz性质。本文仅利用线性代数的基本性质，对这一结果给出了一个新的证明。此外，我们的证明在k的特征大于A的阶的情况下仍然成立，即A 1+A 2+···+A n−n。

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A new proof of Stanley’s theorem on the strong Lefschetz property

. A standard graded artinian monomial complete intersection algebra A = k [ x 1 , x 2 , . . . , x n ] / ( x a 1 1 , x a 2 2 , . . . , x a n n ), with k a ﬁeld of characteristic zero, has the strong Lefschetz property due to Stanley in 1980. In this paper, we give a new proof for this result by using only the basic properties of linear algebra. Furthermore, our proof is still true in the case where the characteristic of k is greater than the socle degree of A , namely a 1 + a 2 + · · · + a n − n .

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来源期刊

Colloquium Mathematicum MATHEMATICS-

CiteScore

0.90

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Colloquium Mathematicum is a journal devoted to the publication of original papers of moderate length addressed to a broad mathematical audience. It publishes results of original research, interesting new proofs of important theorems and research-expository papers in all fields of pure mathematics. Two issues constitute a volume, and at least four volumes are published each year.