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Trace ideals of syzygies
We study the behavior of trace ideals under taking syzygies. In particular, when $R$ is numerical semigroup ring and $I$ is a homogeneous ideal in $R$, we obtain an upper estimate for $\operatorname{tr}_R(Ω^1_R(I))$, and we show this estimate is sharp when $I$ is the conductor ideal $\mathfrak{c}_R$
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