WHEN ARE WEAK
Permutation Polynomials Strong, Sophie Frisch · 1995
For a commutative finite ring with identity R, the two definitions of permutation polynomial in several indeterminates over R coincide if and only if R is a direct sum of finite fields. Amer. Math. Soc. 1991 Mathematics Subject Classification: 11T06, 13M10; Secondary: 13B25. All rings considered are commutative and finite, and ring always means ring with identity. A polynomial f 2 R(x) is said to be a permutation polynomial (abbreviated PP) if the function it defines on R through substitution, r 7! f(r), is a permutation. This notion has been generalized to polynomials in several indeterminates in two dierent ways. We will characterize the rings for which the two coincide. (For quotient rings of the integers this has been done by Kaiser and Nobauer (1).)