THE JACOBI SUMS OVER GALOIS RINGS AND ITS ABSOLUTE VALUES

The Galois ring R of characteristic p(n) having p(mn) elements is a finite extension of the ring of integers modulo p(n), where p is a prime number and n,m are positive integers. In this paper, we develop the concepts of Jacobi sums over R and under the assumption that the generating additive character of R is trivial on maximal ideal of R, we obtain the basic relationship between Gauss sums and Jacobi sums, which allows us to determine the absolute value of the Jacobi sums.