When the associated graded ring of a semigroup ring is Complete Intersection

Details When the associated graded ring of a semigroup ring is Complete Intersection When the associated graded ring of a semigroup ring is Complete Intersection

2011-11-05

arxiv.org/abs/1111.1294v3

Mathematics

Commutative Algebra

23 pages

Scientific paper

Let (R, m) be the semigroup ring associated to a numerical semigroup S. In this paper we study the property of its associated graded ring G(m) to be Complete Intersection. In particular, we introduce and characterize {\beta}-rectangular and {\gamma}-rectangular Ap\'ery sets, which will be the fundamental concepts of the paper and will provide, respectively, a sufficient condition and a characterization for G(m) to be Complete Intersection. Then we use these notions to give four equivalent conditions for G(m) in order to be Complete Intersection.

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