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

Volume 173 / 2023

Ho V. N. Phuong, Quang Hoa Tran Colloquium Mathematicum 173 (2023), 1-8 MSC: Primary 13C40; Secondary 13E10, 14M10. DOI: 10.4064/cm8987-11-2022 Published online: 24 January 2023

Abstract

A standard graded artinian monomial complete intersection algebra $A=\Bbbk [x_1,\ldots ,x_n]/(x_1^{a_1},\ldots ,x_n^{a_n})$, with $\Bbbk $ a field of characteristic zero, has the strong Lefschetz property defined by Stanley in 1980. In this paper, we give a new proof for this result by using only the basic linear algebra. Furthermore, our proof is still valid in the case where the characteristic of $\Bbbk $ is greater than the socle degree of $A$, namely $a_1+\cdots +a_n - n$.

Authors

  • Ho V. N. PhuongUniversity of Sciences
    Hue University
    Hue City, Vietnam
    e-mail
  • Quang Hoa TranUniversity of Education
    Hue University
    Hue City, Vietnam
    e-mail

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