A note on power invariant rings. (1981) - Kim, Joong Ho
Abstract : LetR be a commutative ring with identity andR ( ( n ) ) = R [ [ X 1, …, X n ] ] the power series ring inn independent indeterminatesX 1, …, X n overR .R is called power invariant if wheneverS is a ring such thatR [ [ X 1 ] ] ≅ S [ [ X 1 ] ], thenR ≅ S .R is said to be forever-power-invariant ifS is a ring andn is any positive integer such thatR ( ( n ) ) ≅ S ( ( n ) ) thenR ≅ S LetI C ( R ) denote the set of alla ∈ R such that there isR - homomorphismσ : R [ [ X ] ] → R withσ ( X ) = a . ThenI C ( R ) is an ideal ofR . It is shown that ifI C ( R ) is nil, R is forever-power-invariant