Abstract
In this paper, we give new characterizations of the Buchsbaum and Cohen-Macaulay properties of the tangent cone $\gr_\frakm(R)$, where $(R,\frakm)$ is a numerical semigroup ring of embedding dimension 3. In particular, we confirm the conjectures raised by Sapko on the Buchsbaumness of $\gr_\frakm(R)$.
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