关于S－系的纯性

ON PURITY OF S-ACTS

设Ｓ是么半群，在右Ｓ－系范畴Ａｃｔ－Ｓ中，有两种纯性的概念，分别被Ｎｏｒｍａｋ，Ｇｏｕｌｄ和Ｒｅｎｓｈａｗ所研究．我们分别称之为ＮＧ－纯性和Ｒ－纯性．本文考虑ＮＧ－纯性和Ｒ－纯性的关系．我们证明了ＮＧ－纯性蕴含Ｒ－纯性，并且给出例子说明反过来是不对的．最后我们引入了关系正合序列的概念，并用来研究循环系的Ｒ－纯循环子系的性质．

Let S be a monoid. There exist two definitions of purity of S-acts,say NG-purity and R-purity,which were introduced and studied by Normak and Gould,by Renshaw,respectively. In this paper we consider the relationship between NG-purity and Rpurity. We show that NG-purity implies R-purity,and give an example to show that the converse is not true. We also consider properties of R-pure cyclic S-acts.