International Journal of Mathematics and Mathematical Sciences
Volume 4 (1981), Issue 3, Pages 485-491
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.
Let be a commutative ring with identity and the power series ring in independent indeterminates over . is called power invariant if whenever is a ring such that , then . is said to be forever-power-invariant if is a ring and is any positive integer such that then Let denote the set of all such that there is - homomorphism with . Then is an ideal of . It is shown that if is nil, is forever-power-invariant