IDEAL MAKSIMAL DAN PRIMA DARI GELANGGANG POLINOM MIRING ATAS DAERAH BILANGAN BULAT GAUSS (Makara Journal of Science, 2010)
Maximal and Prime Ideals of Skew Polynomial Ring Over the Gauss Integers Domain. Let R be any ring with identity 1, σ be an automorphism of R and δ be a left σ-derivation. The skew polynomial ring over R in an indeterminate x is the set of polynomials anx n + an-1x n-1 + . . . + a0 where ai∈ R with multiplication rule xa = σ (a) x + δ(a) for all ai∈ R. In this paper, R is Gauss integers, i.e Z + Zi, where i 2 = -1, σ is the automorphism of R with σ(a + bi) = a - bi where a,b∈ Z, the ring of integers, and δ is the zero σ-derivation. We will show maximal and prime ideals of this skew polynomial ring.