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本质子系满足链条件
引用本文:张霞,陈裕群,王燕鸣.本质子系满足链条件[J].东北数学,2006,22(3):357-369.
作者姓名:张霞  陈裕群  王燕鸣
作者单位:School of Mathematics and Computational Science Sun Yat-Sen University,School of Mathematical Sciences,South China Normal University,School of Mathematics and Computational Science,Sun Yat-Sen University,Guangzhou,510275,Guangzhou,510631,Guangzhou,510275
基金项目:国家自然科学基金;国家自然科学基金
摘    要: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.

关 键 词:半群  有限分解  结构表征  群论

Chain Conditions on Essetial Subacts
ZHANG Xia,CHEN Yu-qun,WANG Yan-ming.Chain Conditions on Essetial Subacts[J].Northeastern Mathematical Journal,2006,22(3):357-369.
Authors:ZHANG Xia  CHEN Yu-qun  WANG Yan-ming
Institution:[1]School of Mathematics and Computational Science, Sun Yat-Sen University, Guangzhou, 510275 [2]School of Mathematical Sciences, South China Normal University, Guangzhou, 510681
Abstract: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.
Keywords:essential subact  chain condition  PS-act  CS-act
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