Polynomial Decomposition Over Rings.

Polynomial Decomposition;Number Theory;Algebra;Ring Theory;Polynomial;Mathematics;Science;Mathematics

Wyman, Brian KennethSmith, Karen E. ;

University of Michigan

关键词: Polynomial Decomposition;    Number Theory;    Algebra;    Ring Theory;    Polynomial;    Mathematics;    Science;    Mathematics;   

Others  :  https://deepblue.lib.umich.edu/bitstream/handle/2027.42/77772/bkwyman_1.pdf?sequence=1&isAllowed=y

瑞士|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

We study of the arithmetic of polynomials under the operation of functional composition, namely, the operation of functional compositon:f(x) ∘ g(x) := f(g(x)).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 ℤ.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.