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

Bahareh Lajmiri, Farhad Rahmati

DOI Number
https://doi.org/10.22190/FUMI2001131L
First page
131
Last page
140

Abstract


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 $u=x_ix_n, t+1\leq i\leq n-t.$ Indeed, $I$ has the property that $\Ass(I^m)=\Ass(I)$ for all $m\geq 1$ and $i\leq t,$ 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.  

Keywords

Monomial ideals, t-spread principal Borel ideals, Arithmetical rank, Complete intersection.

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References


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DOI: https://doi.org/10.22190/FUMI2001131L

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