On the associated graded ring of a semigroup ring
M D'ANNA, V Micale, A Sammartano - Journal of Commutative Algebra, 2011 - JSTOR
M D'ANNA, V Micale, A Sammartano
Journal of Commutative Algebra, 2011•JSTORLet (𝑅, 𝐦) be a numerical semigroup ring. In this paper we study the properties of its
associated graded ring 𝐺 (𝐦). In particular, we describe the HM 0 for 𝐺 (𝐦)(where ℳ is the
homogeneous maximal ideal of 𝐺 (𝐦)) and we characterize when 𝐺 (𝐦) is Buchsbaum.
Furthermore, we find the length of HM 0 as a 𝐺 (𝐦)-module, when 𝐺 (𝐦) is Buchsbaum. In
the 3-generated numerical semigroup case, we describe the HM 0 in terms of the Apery set
of the numerical semigroup associated to 𝑅. Finally, we improve two characterizations of the …
associated graded ring 𝐺 (𝐦). In particular, we describe the HM 0 for 𝐺 (𝐦)(where ℳ is the
homogeneous maximal ideal of 𝐺 (𝐦)) and we characterize when 𝐺 (𝐦) is Buchsbaum.
Furthermore, we find the length of HM 0 as a 𝐺 (𝐦)-module, when 𝐺 (𝐦) is Buchsbaum. In
the 3-generated numerical semigroup case, we describe the HM 0 in terms of the Apery set
of the numerical semigroup associated to 𝑅. Finally, we improve two characterizations of the …
Abstract
Let (𝑅, 𝐦) be a numerical semigroup ring. In this paper we study the properties of its associated graded ring 𝐺(𝐦). In particular, we describe the for 𝐺(𝐦) (where ℳ is the homogeneous maximal ideal of 𝐺(𝐦)) and we characterize when 𝐺(𝐦) is Buchsbaum. Furthermore, we find the length of as a 𝐺(𝐦)-module, when 𝐺(𝐦) is Buchsbaum. In the 3-generated numerical semigroup case, we describe the in terms of the Apery set of the numerical semigroup associated to 𝑅. Finally, we improve two characterizations of the Cohen-Macaulayness and Gorensteinness of 𝐺(𝐦) given in [2, 3], respectively.
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