When do two networks have the same steady-state ideal?

Chemical reaction networks are often used to model and understand biological processes such as cell signaling. Under the assumption of mass action kinetics, reaction networks give rise to polynomial dynamical systems. The ideals generated by these polynomials are called steady-state ideals. Steady-state ideals appear in multiple contexts within the chemical reaction network literature, however they have yet to be systematically studied. To begin such a study, we ask and partially answer the following question: when do two reaction networks give rise to the same steady-state ideal? In this talk, we will describe three operations on the reaction networks that preserve the steady-state ideal. Furthermore, we will describe combinatorial conditions to identify monomials in a steady-state ideal.