On Finite Dimension of a Kind of Generalized Power Series Rings

Let R be a perfect and coherent commutative ring with unit element,in this paper the relationship between the finitistic dimensions of R and the generalized power series ring R^≤,Sover R was investigated,and some inequalities for finitistic dimensions were obtained.Resultsshow that the finitistic projective(injective) dimension of R is less than and equal to the finitistic projective(injective)dimension of R^≤,Sand the finitistic weak dimension of R is less than and equal to the finitistic weak dimension of R^≤,S.