ABSTRACT
A domain is called a divided domain if each of its prime ideals is divided in the domain; and “locally divided domains” are defined in the natural way. Divided prime ideals have arisen in the Greenberg-Vasconcelos theory of umbrella rings and the quasilocal rings of global dimension. This chapter shows that, with regard to the calculation of weak global dimension, certain LPVDs behave like Noetherian rings.
