Independence of elements in a ring and the height of the ideal they generate
Abstract
We discuss three closely connected topics concerning the independence of elements in a commutative ring and the height of the ideal they generate. The first topic discussed is the relative independence of elements in a commutative ring. We start by considering a general ring and then specialize it to a local ring and in particular to and a power series ring, comparing the notion of relative independence to that of regular sequence, system of parameters and analytic independence respectively. Then, concentrating in the power series ring, we consider a condition under which power series are analytically independent. As the final topic we analyze the behavior of the height of an ideal in polynomial and power series extensions.
Degree
Ph.D.
Advisors
Abhyankar, Purdue University.
Subject Area
Mathematics
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