## Polynomial MappingsThe 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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absolute values algebraic integers algebraic number field algebraically closed arbitrary assertion follows assume commutative ring cycle of length cyclic points D-ring D.L. McQUILLAN Dedekind domain defined deg f denote divides divisible elements equals exists f e Z[X finite extension finite norm property finitely generated ideal fixpoints fractional ideal hence holds ideal of Int(Z implies infinite integer-valued polynomials invertible J.-L.CHABERT Lemma Math maximal ideal mod q monic polynomial Noetherian domain non-zero observe obtain p-adic Pólya field polynómes à valeurs polynomial f polynomial mapping polynomial of degree prime ideals prime power PROOF property SP Prove Prüfer domain purely transcendental extensions R-module rational functions rational integers rational number rational prime representation ring result ring Int(R ring of integers satisfying sequence shows Skolem ring subset suitable unique factorization domain valeurs entières variables W.NARKIEwicz zero characteristics