2018/06/30 by Herzog, Jürgen, Watanabe, Kei-ichi
#Commutative Algebra (math.AC) #FOS: Mathematics
paper · doi:10.48550/arxiv.1807.00134
We study almost symmetric numerical semigroups and semigroup rings. We describe a characteristic property of the minimal free resolution of the semigroup ring of an almost symmetric numerical semigroup. For almost symmetric semigroups generated by 4 elements we will give a structure theorem by using the \lq\lq row-factorization matrices", introduced by Moscariello. As a result, we give a simpler proof of Komeda's structure theorem of pseudo-symmetric numerical semigroups generated by 4 elements. Row-factorization matrices are also used to study shifted families of numerical semigroups.