A standard graded artinian monomial complete intersection algebra
A=k[x1β,x2β,β¦,xnβ]/(x1a1ββ,x2a2ββ,β¦,xnanββ), 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 a1β+a2β+β―+anββn