Vol. 51, No. 1, 1974

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 307: 1  2
Vol. 306: 1  2
Vol. 305: 1  2
Vol. 304: 1  2
Vol. 303: 1  2
Vol. 302: 1  2
Vol. 301: 1  2
Vol. 300: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Editorial Board
Subscriptions
Officers
Special Issues
Submission Guidelines
Submission Form
Contacts
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Author Index
To Appear
 
Other MSP Journals
Power invariant rings

Joong Ho Kim

Vol. 51 (1974), No. 1, 207–213
Abstract

A ring A is called power invariant if whenever B is a ring such that the formal power series rings A[[X]] and B[[X]] are isomorphic, then A and B are isomorphic. A ring A is said to be strongly power invariant if whenever B is a ring and ϕ is an isomorphism of A[[X]] onto B[[X]], then there exists a B-automorphism ψ of B[[X]] such that ψ(X) = ϕ(X). Strongly power invariant rings are power invariant. For any commutative ring A,A∕J(A)n is strongly power invariant, where J(A) is the Jacobson radical of A, and n is any positive integer. A left or right Artinian ring is strongly power invariant. If A is a left or right Noetherian ring, then A[t], the polynomial ring in an indeterminate t over A, is strongly power invariant.

Mathematical Subject Classification 2000
Primary: 16A48
Secondary: 13J05
Milestones
Received: 15 November 1972
Published: 1 March 1974
Authors
Joong Ho Kim