Georgia Institute of Technology College of Sciences

One way to analyze a (finitely generated) module over a ring is to consider its minimal free resolution and look at its Betti table. The Betti table would be obtained by algebraic computations in general, but in case of the ideal (consists of relations) is generated by monomial quadratics, we can obtain Betti numbers (which are entries of the Betti table) by looking at the corresponding graphs and its associated simplicial complex. In this talk, we will introduce the Stanley-Reisner ideal which is the ideal generated by monomial quadratics and Hochster’s formula. Also, we will deal with some theorems and corollaries which are related to our topic.