2017/10/19 by Gimenez, Philippe, Srinivasan, Hema · 1 citation
#13A02 #13D02 #14H50 #20M14 #20M25 #Commutative Algebra (math.AC) #FOS: Mathematics
paper · doi:10.48550/arxiv.1710.07237
We construct a minimal free resolution of the semigroup ring k[C] in terms of minimal resolutions of k[A] and k[B] when is a numerical semigroup obtained by gluing two numerical semigroups and <b>. Using our explicit construction, we compute the Betti numbers, graded Betti numbers, regularity and Hilbert series of k[C], and prove that the minimal free resolution of k[C] has a differential graded algebra structure provided the resolutions of k[A] and k[B] possess them. We discuss the consequences of our results in small embedding dimensions. Finally, we give an extension of our main result to semigroups in Nn</b>