The Filtration Dimensions of Generalized Power Series Algebras
Received:November 19, 2012  Revised:June 04, 2013
Key Words: standardly stratified algebra   generalized power series algebra   generalized power series module   filtration dimension.
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).
 Author Name Affiliation Hailou YAO College of Applied Sciences, Beijing University of Technology, Beijing 100124, P. R. China Ying GUO College of Applied Sciences, Beijing University of Technology, Beijing 100124, P. R. China
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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.