R-automorphisms of R[t][[X]]

Joong Ho Kim

Vol. 42 (1972), No. 1, 81–88

DOI: 10.2140/pjm.1972.42.81

Abstract

Let R be a commutative ring with identity, R[t] the polynomial ring in an indeterminate t over R, and R[t][[X]] the formal power series ring in an indeterminate X over R[t]. Let α = ∑ _i=1^∞a_i(t)Xⁱ and β = ∑ _i=0^∞b_i(t)Xⁱ be elements of R[t][[X]] where a_i(t) and b_i(t) are elements of R[t] for each i. This paper gives necessary and sufficient conditions in order that there exist an R-automorphism of R[t][[X]] mapping t and X onto α and β respectively.

Mathematical Subject Classification 2000

Primary: 13B10

Secondary: 13J05

Milestones

Received: 30 March 1971

Published: 1 July 1972