S-系上的本质同余与富余同余

本文给出了S-系上本质同余与富余同余的概念,并刻画了它们的性质;利用与模论中研究本质子模与余子模相类似的方法,得到了与其相类似的结果.     

本质子系满足链条件

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.     

可分解半群的Morita等价

设S,R是可分解半群.记US-FAct={sM∈S-Act|SM=M且SHoms(S,M)≌M],给出了范畴US-FAct与UR-FAct等价的刻划;S分别强Morita等价于一个夹层半群、局部单位半群、幺半群和群的条件;S是完全单半群当且仅当S强Morita等价于一个群且对任何指标集I,S SHoms(S,i∈I S)→i∈I S,s t·f→(st)f,是同构.     

投射和不可分S-系 *

给出了投射酉S -系和投射不可分酉S 系的结构 ,从而推广了一些相关的结果.