论文标题
斯坦利定理的新证明
A new proof of Stanley's theorem on the strong Lefschetz property
论文作者
论文摘要
标准分级的Artinian单位完整交叉分子代数$ a = \ bbbk [x_1，x_2，\ ldots，x_n]/（x_1^{a_1}，x_2^{a_2} {a_2}，\ ldots，\ ldots，\ ldots，x_n^{a_n^{a_n}）在1980年由于斯坦利而导致的属性。在本文中，我们仅使用线性代数的基本属性给出了新的证明。此外，在$ \ bbbk $的特征大于$ a $的SOCLE $，即$ a_1+a_1+a_2+\ cdots+a_n -n $的情况下，我们的证明仍然是正确的。
A standard graded artinian monomial complete intersection algebra $A=\Bbbk[x_1,x_2,\ldots,x_n]/(x_1^{a_1},x_2^{a_2},\ldots,x_n^{a_n})$, with $\Bbbk$ 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 $\Bbbk$ is greater than the socle degree of $A$, namely $a_1+a_2+\cdots+a_n - n$.
