On Reciprocal Extensions R[α + α⁻¹] of R

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 ϕ_α(−λ)/ϕ_α(λ)(λ ∈ U(R)), where ϕ_α(X) ∈ K[X] is the minimal monic polynomial of α.

Key Words:

• Simple extensions
• Anti-integral
• Units

Acknowledgments