Abstract
The central objective of this project is to study the Hilbert Theorem via Syzygy Modules, also known as Hilbert's Syzygy Theorem. This result deals with the existence of a free resolution for finitely generated R modules, where R is a ring of polynomials in a field K in the variables X_1, X_2, ..., X_n. In addition, we intend to apply this theory to explore examples using the free SINGULA…