Polynomial Mappings

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Springer, Nov 14, 2006 - Mathematics - 140 pages
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The book deals with certain algebraic and arithmetical questions concerning polynomial mappings in one or several variables. Algebraic properties of the ring Int(R) of polynomials mapping a given ring R into itself are presented in the first part, starting with classical results of Polya, Ostrowski and Skolem. The second part deals with fully invariant sets of polynomial mappings F in one or several variables, i.e. sets X satisfying F(X)=X . This includes in particular a study of cyclic points of such mappings in the case of rings of algebrai integers. The text contains several exercises and a list of open problems.
 

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Contents

RINGS OF INTEGRALVALUED POLY NOMIALS
1
FIXED DIVISORS
26
INTEGRALVALUED DERIVATIVES
41
FULLY INVARIANT SETS FOR POLY NOMIAL
67
PAIRS OF POLYNoMIAL MAPPINGs
93
LIST OF OPEN PROBLEMs
110
INDEX
124
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