Non-Level O-sequences of Codimension 3 and Degree of The Socle Elements

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dc.creatorShin, Yong Su
dc.date2005-05-08
dc.date.accessioned2026-07-07T05:19:41Z
dc.date.available2026-07-07T05:19:41Z
dc.descriptionIt is unknown if an Artinian level O-sequence of codimension 3 and type $r (\ge 2)$ is unimodal, while it is known that any Gorenstein O-sequence of codimension 3 is unimodal. We show that some Artinian non-unimodal O-sequence of codimension 3 cannot be level. We also find another non-level case: if some Artinian algebra $A$ of codimension 3 has the Hilbert function $$\begin{matrix}\H & : & h_0 & h_1 & ... & h_{d-1} & \underbrace{h_d ... h_d}_{s\text{-times}} & h_{d+s}, \end{matrix} $$ such that $h_d<h_{d+s}$ and $s\ge 2$, then $A$ has a socle element in degree $d+s-2$, that is, $A$ is not level.
dc.identifierhttps://arxiv.org/abs/math/0505132
dc.identifierhttp://arxiv.org/abs/math/0505132
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/75110
dc.subjectCommutative Algebra
dc.subject13D40; 4M10
dc.titleNon-Level O-sequences of Codimension 3 and Degree of The Socle Elements
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