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 subact...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.展开更多
基金The NSF (10571181,10471045) of Chinathe NSF (021073, Z02017) of Guangdong Province
文摘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.
