A note on power invariant rings

[摘要] LetRbe a commutative ring with identity andR((n))=R[[X1,…,Xn]]the power series ring innindependent indeterminatesX1,…,XnoverR.Ris called power invariant if wheneverSis a ring such thatR[[X1]]≅S[[X1]], thenR≅S.Ris said to be forever-power-invariant ifSis a ring andnis any positive integer such thatR((n))≅S((n))thenR≅SLetIC(R)denote the set of alla∈Rsuch that there isR- homomorphismσ:R[[X]]→Rwithσ(X)=a. ThenIC(R)is an ideal ofR. It is shown that ifIC(R)is nil,Ris forever-power-invariant

[学科分类] 数学（综合）