On free resolutions of some semigroup rings

Abstract

For some numerical semigroup rings of small embedding dimension, namely those of embedding dimension 3, and symmetric or pseudosymmetric of embedding dimension 4, presentations has been determined in the literature. We extend these results by giving the whole graded minimal free resolutions explicitly. Then we use these resolutions to determine some invariants of the semigroups and certain interesting relations among them. Finally, we determine semigroups of small embedding dimensions which have strongly indispensable resolutions. (C) 2013 Elsevier B.V. All rights reserved

The structure of the minimal free resolution of semigroup rings obtained by gluing

“…This was also obtained independently in [3]. Moreover, one can find in [13] a way to build families of numerical semigroups of embedding dimension 4 that are Gorenstein and not complete intersections.…”

Quadratic numerical semigroups and the Koszul property

“…If H is not CI, we employ the following characterization found by Bresinsky [4], as given by Barucci et al in [3,Theorem 3].…”

On pseudo symmetric monomial curves

“…The numbers b j and c j above can be obtained from the maps φ 2 and φ 3 as in [6,Corollary 16]. For instance, the S-degrees of the non-zero entries in the first column of φ 2 gives us b…”

“…In section two, we determine indispensable binomials of I S and prove that K[S] has a strongly indispensable minimal S-graded free resolution if and only if α 4 > 2 and α 1 − α 21 > 2, see Theorem 2.6, filling a missing case in [6].…”