Isomorphic power series rings

M. J. O’Malley

Vol. 41 (1972), No. 2, 503–512

DOI: 10.2140/pjm.1972.41.503

Abstract

Let A and B be commutative rings with identity, let X be an indeterminate over A and B, and let A[[X]] and B[[X]] be the formal power series rings over A and B, respectively. The motivation for this paper was to consider the analogue of a question raised by Coleman and Enochs for the polynomial ring. Specifically, the following question is considered: (∗) If A[[X]]≅B[[X]], must A≅B? (The author knows no counterexample.)

Mathematical Subject Classification 2000

Primary: 13J05

Milestones

Received: 28 January 1971

Revised: 12 August 1971

Published: 1 May 1972