Let I be an m-generated complete intersection monomial ideal inWe also study the upper-discrete structure for monomial ideals and prove that if I is a squarefree monomial ideal minimally generated by 3 elements, then the Stanley depth of I is n − 1.

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We investigate the Rees algebra and the toric ring of the squarefree monomial ideal associated to the three-dimensional Ferrers diagram. Under the projection property condition, we describe explicitly the presentation ideals of the Rees algebra and the toric ring. We show that the toric ring is a Koszul Cohen-Macaulay normal domain, while the Rees algebra is Koszul and the defining ideal is of fiber type.

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