Maximal and Prime Ideals of Skew Polynomial Ring Over the Gauss Integers Domain

Abstract

Maximal and Prime Ideals of Skew Polynomial Ring Over the Gauss Integers Domain. Let R be any ring withidentity 1, σ be an automorphism of R and δ be a left σ-derivation. The skew polynomial ring over R in anindeterminate x is the set of polynomials anxn + an-1xn-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 i2 = -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 thisskew polynomial ring.

Keywords

• Gauss integers
• maximal ideal
• prime ideal
• skew polynomial ring