Polynomial decomposition over rings
by Wyman, Brian Kenneth, Ph.D., UNIVERSITY OF MICHIGAN, 2010, 69 pages; 3429315

Abstract:

We study of the arithmetic of polynomials under the operation of functional composition, namely, the operation fx&j0;gx :=fgx . This topic has a rich history when the polynomials have coefficients in fields, but prior to this work, relatively little was known when the polynomials had coefficients in more general rings. Indeed, most of the classical problems in this area were open even over [special characters omitted]! We develop a theory of polynomial composition (and decomposition) over rings, providing several ring-analogs to well-known field results. We also provide new, elementary proofs of some results over fields, and we exhibit examples and counterexamples over rings in an attempt to define our methods' successes and limitations.

 
AdviserMichael Zieve
SchoolUNIVERSITY OF MICHIGAN
SourceDAI/B 71-11, p. , Nov 2010
Source TypeDissertation
SubjectsMathematics; Theoretical mathematics
Publication Number3429315
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