The Short Resolution of a Semigroup Algebra

Abstract

Abstract. This work generalizes the short resolution given in Proc. Amer. Math. Soc. 131, 4, (2003), 1081-1091, to any affine semigroup. Moreover, a characterization of Apéry sets is given. This characterization lets compute Apéry sets of affine semigroups and the Frobenius number of a numerical semigroup in a simple way. We also exhibit a new characterization of the Cohen-Macaulay property for simplicial affine semigroups.

Simplicial affine semigroups with monomial minimal reduction ideals

“…We close this section by a formula for the Castelnouvo-Mumford regularity of gr m (R), when m has monomial minimal reduction and gr m (R) is Cohen-Macaulay. As a consequence, we get another proof of [14,Corollary 4.9]. Note that in the statement of [14,Corollary 4.9] there is a typo, indeed reg(I S ) should be reg(I S ) − 1 = reg(R).…”

“…As a consequence, we get another proof of [14,Corollary 4.9]. Note that in the statement of [14,Corollary 4.9] there is a typo, indeed reg(I S ) should be reg(I S ) − 1 = reg(R). Example 4.15.…”

“…The argument in the proof of[14, Corollary 4.7] provides another perspective of Lemma 1.5(b). It is shown that R is Cohen-Macaulay if and only if it is a free K[z 1 , .…”

Critical Binomial Ideals of Northcott Type

“…, 0, −1). Now, our claim follows from the results in [14, Section 3] or, more directly, by [22,Theorem 3], by just taking into account that the initial ideal of I A , with respect to an A-graded reverse lexicographical term order such that x n is the least variable, is spanned by…”

“…It is well known that every minimal system of generators of a toric ideal has the same cardinal (see, for instance, [22,Section 2]). Now, if I ⊂ k[x 1 , .…”