Abstract
The local rings of global dimension two are characterized. Such rings are either noetherian rings, valuation rings, or the so-called umbrella rings, A local ring A is an umbrella ring if and only if A contains a prime ideal P such that: 1. (a) A p is a valuation ring of global dimension one or two, 2. (b) A P is a regular local ring of global dimension two, 3. (c) PA p = P, 4. (d) A has only countably many principal prime ideals. These results are generalized by defining an F-ring to be a domain A containing a prime ideal Q such that A Q is a valuation ring and QA Q = Q. We show that A is the fiber-product of A Q and A Q over A Q QA Q and determine the global dimension of A in terms of the global dimensions of A Q and A Q .
Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
