International Journal of Mathematics and Mathematical Sciences
Volume 4 (1981), Issue 3, Pages 485-491

A note on power invariant rings

Joong Ho Kim

Department of Mathematics, East Carolina University, Greenville 27834, N.C., USA

Received 1 September 1980

Copyright © 1981 Joong Ho Kim. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Let R be a commutative ring with identity and R((n))=R[[X1,,Xn]] the power series ring in n independent indeterminates X1,,Xn over R. R is called power invariant if whenever S is a ring such that R[[X1]]S[[X1]], then RS. R is said to be forever-power-invariant if S is a ring and n is any positive integer such that R((n))S((n)) then RS Let IC(R) denote the set of all aR such that there is R- homomorphism σ:R[[X]]R with σ(X)=a. Then IC(R) is an ideal of R. It is shown that if IC(R) is nil, R is forever-power-invariant