Automorphisms of algebras of restricted formal series (Q1901986)

Let \({\mathfrak p}\) be a no-nilpotent ideal of a unitary commutative ring \(A\), \(X\) an indeterminate. \(A \{{\mathfrak p} X\}\), the restricted power series ring for \({\mathfrak p}\), is the subring of \(A[[X]]\) formed by the series the coefficients of which tend to zero in the \({\mathfrak p}\)-adic topology of \(A\). We determine the invertible elements of \(A \{{\mathfrak p}, X\}\). If \(f = \sum^\infty_{i = 0} a_i X^i \in A \{{\mathfrak p}, X\}\), necessary and sufficient conditions on \(f\) are given to assure that there exists a \(A\)-automorphism of \(A \{{\mathfrak p}, X\}\) sending \(X\) to \(f\). Any \(A\)-endomorphism of \(A \{{\mathfrak p}, X\}\) is uniquely determined by its action on \(X\).