3:30pm4:45pm, Seminar Hall Resolutions of some semigroup rings Hema Srinivasan University of Missouri, USA. 151018 Abstract Let denote the semigroup of natural numbers (including zero) under addition. Sub semigroups of with a finite number of gaps are called the numerical semigroups. Let $G =< C >$ be a numerical semigroup minimally generated by a subset $C = (c_1, . . . , c_n)$ of relatively prime integers in . If $k$ is a field, then $S = k[t^aa \in G]$ is called the semigroup ring associated to $G$. This semigroup ring $S$ is isomorphic to $k[x_1, . . . , x_n]/I_C = R/I_C$ where $I_C$ is the kernel of the map $\phi : k[x_1,...,x_n] \rightarrow S$ given by $\phi (xi) = t^{c_i}. The minimal $R$âˆ’free resolution of $S$ are known only when either $n$ is small or when $C$ is special in some way. We will illustrate the known results via a series of examples and explicitly demonstrate their resolutions and other numerical invariants such as Betti numbers, Hilbert Series, Regularity and Frobenius numbers.
