Advances in Commutative Ring Theory (Proc. of 1997 Fez Conf)

Lecture Notes in Pure and Appl. Mathematics 205, Dekker 1999,

pp 323-336.

We also summarize and generalize the known results on the number of functions and the number of permutations on a finite ring induced by polynomials with coefficients in the ring itself; and for a finite commutative local ring whose maximal ideal is of nilpotency 2, we also determine the structure of the semigroup of functions and of the group of permutations induced on R by polynomials in R[x].

1991 Mathematics Subject Classification:

Primary 13M10, 13B25; Secondary: 11C08, 13F05, 11T06.

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