Non-Level O-sequences of Codimension 3 and Degree of The Socle Elements
Shin, Yong Su
Original · EN
It is unknown if an Artinian level O-sequence of codimension 3 and type r (≥ 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 matrix &: & h₀ & h₁ &... & hd₋₁ & hd... hds-times & hd₊ₛ, matrix such that hd<hd₊ₛ and s≥ 2, then A has a socle element in degree d+s-2, that is, A is not level.
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