Let R be a finite commutative ring. The set F(R) of polynomialfunctions on R is a finite commutative ring with pointwise operations. Its group of units F(R)(x) is just the set of all unit-valued polynomial functions....
详细信息
Let R be a finite commutative ring. The set F(R) of polynomialfunctions on R is a finite commutative ring with pointwise operations. Its group of units F(R)(x) is just the set of all unit-valued polynomial functions. We investigate polynomial permutations on R[x]/(x(2)) = R[alpha], the ring of dual numbers over R, and show that the group P-R(R[alpha]), consisting of those polynomial permutations of R[alpha] represented by polynomials in R[x], is embedded in a semidirect product of F(R)(x) by the group P(R) of polynomial permutations on R. In particular, when R = F-q, we prove that P-Fq(F-q[alpha]) congruent to P(F-q) (sic)(theta) F(F-q)(x). Furthermore, we count unit-valued polynomial functions on the ring of integers modulo p(n) and obtain canonical representations for these functions.
暂无评论