Fund Project:Supported by the National Natural Science Foundation of China (Grant Nos.10971172; 11271119) and the Natural Science Foundation of Beijing (Grant No.1122002).
In this paper, we study the properties of generalized power series modules and the filtration dimensions of generalized power series algebras. We obtain that $[[\triangle ^{S,\leq}]]$-${\rm gfd}([[A^{S,\leq}]])=\triangle$-${\rm gfd}(A)$ if $A$ is an $R$-module where $R$ is a perfect and coherent commutative algebra, and $(R,\leq)$ is standardly stratified.
