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Permutation polynomials in several variables over residue class rings. (English) Zbl 0644.13003
There are two ways in generalizing the concept of permutation polynomial functions (PPFs) over a commutative ring R with 1 to multiplaced functions, namely $$k$$-ary PPFs and strict $$k$$-ary PPFs. These can be defined as polynomial functions $$f: R^ k\to R$$ for which k-ary functions (resp. polynomial functions) $$f_ 2,...,f_ k$$ over $$R$$ exist, such that the $$k$$-tuple $$(f,f_ 2,...,f_ k)$$ represents a permutation of $$R^ k$$. It is shown that if R is isomorphic to the direct product $$\times^{n}_{i=1}{\mathbb{Z}}_{p_ i^{e_ i}}$$ then these two concepts coincide if and only if all $$e_ i=1$$.
Reviewer: G.Kowol

##### MSC:
 13B25 Polynomials over commutative rings 13F20 Polynomial rings and ideals; rings of integer-valued polynomials 05A05 Permutations, words, matrices
##### Keywords:
residue class ring; permutation polynomial functions