A Counterexample to Polynomial Stability of Hamilton–Marley Cohen–Macaulay Rings

Abstract

In recent years, modules over non-Noetherian rings and their homological algebra have become important objects of study in commutative algebra. In this talk, we discuss Cohen–Macaulayness in the sense of Hamilton–Marley, or HMCMness, which is one of the main approaches to formulating Cohen–Macaulayness for rings that are not necessarily Noetherian. In particular, we construct an example showing that, unlike in the Noetherian case, the property of being an HMCM ring is not necessarily preserved under polynomial extension. This gives a counterexample to the polynomial stability of HMCMness. This seminar is based on the preprint (arXiv:2606.25384).