Automorphisms of Ideals of Polynomial Rings

Let R be a commutative integral domain with unit, f be a nonconstant monic polynomial in R [ t ], and I_f ⊂ R[t] be the ideal generated by f . In this paper we study the group of R -algebra automorphisms of the R -algebra without unit I_f . We show that, if f has only one root (possibly with multiplicity), then Aut(I_f) ≅ R^× . We also show that, under certain mild hypothesis, if f has at least two different roots in the algebraic closure of the quotient field of R , then Aut(I_f) is a cyclic group and its order can be completely determined by analyzing the roots of f .