No abstract

For a reduced one-dimensional complete local k-algebra R, Huneke et al. (Res. Math. Sci., 8(4), paper no. 60, 2021) introduced an important invariant, the reduced type. In this article, we study the extremal behavior of reduced type of some special numerical semigroup rings. For a numerical semigroup ring, the behavior of reduced type can be studied by analyzing the set of pseudo-Frobenius elements of the numerical semigroup. We give complete descriptions of pseudo-Frobenius elements of Bresinsky's numerical semigroups and duplication of numerical semigroups. Further, we explore the extremal behavior of reduced type for the associated semigroup rings.

In the original online version of this article there was an error in the heading: 5 Syzygies of k[Sa,d,k]. The corrected sentence is as follows: 5 Syzygies of K[Sa,d,k].There was also an error in the reference: 7.

Let [Formula: see text] be a numerical semigroup minimally generated by an almost arithmetic sequence. We give a description of a possible row-factorization (RF) matrix for each pseudo-Frobenius element of [Formula: see text] Further, when [Formula: see text] is symmetric and has embedding dimension four or five, we prove that the defining ideal is minimally generated by RF-relations.