A note on denominator ideals of linear fractional transforms of an anti-integral element over an integral domain

抄録

Let α be an anti-integral element of degree t over an integral domain R and φ_α(X) the minimal polynomial of α over the quotient field of R. Let β be a linear fractional transform of α, that is,
β=cα-d/aα-b(a, b, c, d∈R, ad-bc∈R^*)
where R^* is the group of units of R. First we describe I_[β], the denominator ideal of β, in terms of I_[α] and φ_α(a, b) where φ_α(X, Y)=X^tφ_α(Y/X). Next we introduce the ideal ˜{I}_[α] concerning integral property of α and α^-1. Then we describe ˜{I}_[β] by using I_[α], φ_α(a, b) and φ_α(c, d).