PROPERTIES OF $T$-SPREAD PRINCIPAL BOREL IDEALS GENERATED IN DEGREE TWO

摘要

In this paper, we have studied the stability of $t$ -spread principal Borel ideals in degree two. We have proved that $Ass^infty(I) =Min(I)cup {mathfrak{m}}$ , where $I=B_t(u)subset S$ is a $t$ -spread Borel ideal generated in degree $2$ with $u=x_ix_n, t+1leq ileq n-t.$ Indeed, $I$ has the property that $Ass(I^m)=Ass(I)$ for all $mgeq 1$ and $ileq t,$ in other words, $I$ is normally torsion free. Moreover, we have shown that $I$ is a set theoretic complete intersection if and only if $u=x_{n-t}x_n$ . Also, we have derived some results on the vanishing of Lyubeznik numbers of these ideals. ? ?