International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 1981 / Article

Open Access

Volume 4 |Article ID 372713 | https://doi.org/10.1155/S0161171281000343

Joong Ho Kim, "A note on power invariant rings", International Journal of Mathematics and Mathematical Sciences, vol. 4, Article ID 372713, 7 pages, 1981. https://doi.org/10.1155/S0161171281000343

A note on power invariant rings

Received01 Sep 1980

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 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

Copyright © 1981 Hindawi Publishing Corporation. 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.


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