Coherent Rings with Finite Weak Global Dimension

One notable outcome, characterized by homological techniques, is the demonstration that a regular local ring is a Unique Factorization Domain (UFD) (see Corollary 9.1.15). Following Chase’s work in 1960, numerous significant results in the homology theory of Noetherian rings were successfully extended to coherent rings. Vasconcelos provided an exemplary characterization of local rings with a global dimension of two. In this chapter, we aim to delve deeper into the properties of local rings with weak global dimension two, utilizing both homological techniques and methods from star operation theory.