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Let S be a semigroup with zero and an S-act be a centered left S-act.This paper is devoted to the study of chain conditions on PS-acts. We prove that a PS-act having finite decomposition has ACC (DCC) on all subacts if it has ACC (DCC) on essential subacts. Moreover, a PS-act with ACC (DCC) on essential subacts has ACC (DCC) on all subacts if and only if it has finite decomposition.We characterize the structure of a PS-act and generalize some results of the Goldie dimension and semisimple S-acts.