Abstract
When α is an anti-integral element over an integral domain R with quotient field K, we investigate the extensions R ⊆ R[α] and R ⊆ R[α + α−1] ⊆ R[α, α−1]. Further we study some properties of elements ϕα(−λ)/ϕα(λ)(λ ∈ U(R)), where ϕα(X) ∈ K[X] is the minimal monic polynomial of α.
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