International Journal of Mathematics and Mathematical Sciences
Volume 4 (1981), Issue 3, Pages 485-491
doi:10.1155/S0161171281000343
A note on power invariant rings
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.
Abstract
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 R≅S. 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 R≅S Let IC(R) denote the set of all a∈R 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