Non-noetherian krull domains issued from symbolic blow-up and rees algebras

(2005) Non-noetherian krull domains issued from symbolic blow-up and rees algebras. Masters thesis, King Fahd University of Petroleum and Minerals.


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English Abstract

Since Seidenberg's work on the dimension of polynomial rings in 1952, we know that Noetherian domains have the Krull dimension coincide with the valuative dimension (i.e., are Jaffard domains in non-Noetherian jargon). It is still an open problem to know whether this holds for arbitrary finite-dimensional Krull domains. However, non-Noetherian finite-dimensional Krull domains are rare in the literature and all happen to be Jaffard. Some of them arise as symbolic blow-up algebras or symbolic Rees algebras. Our purpose in this MS thesis is to have a close look at various works on this subject, towards a better understanding of non-Noetherian finite-dimensional Krull structures; particularly, those issued from blow-up and Rees algebras.

Item Type: Thesis (Masters)
Subjects: Math
Department: College of Computing and Mathematics > Mathematics
Committee Advisor: Kabbaj, Salah-Eddine
Committee Members: Azad, Hassan and Mimouni, Abdeslam
Depositing User: Mr. Admin Admin
Date Deposited: 22 Jun 2008 14:06
Last Modified: 01 Nov 2019 14:01