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.


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