纯满同态的推广对条件(P′)与条件(P_E)的刻画  

Characterizations of condition(P′) and condition(P_E) by generalizations of pure epimorphisms

作　　者：乔虎生[1] 杨丽丽[1] 

机构地区：[1]西北师范大学数学与统计学院,甘肃兰州730070

出　　处：《西北师范大学学报（自然科学版）》2015年第2期1-3,8,共4页Journal of Northwest Normal University(Natural Science)

基　　金：国家自然科学基金资助项目(11461060);甘肃省高校基本科研业务费项目

摘　　要：设S是幺半群,n是一个正整数.设ψ:X→Y是S-满同态,如果ψ是2-纯的,X满足条件(P),那么Y满足条件(P),但反之未必成立.本文给出了纯满同态的一些新推广.利用这些新概念,我们给出了条件(P′)与条件(PE)的等价刻画,即S-系Y满足条件(P′)的充分必要条件是每个满同态X→Y是弱2-纯的,S-系Y满足条件(PE)的充分必要条件是每个满同态X→Y是PE-2-纯的.最后,研究了新满同态的有向上极限.Let S be a monoid and n apositive integer.Let ψ：X →Y be an S-epimorphism in which X satisfies condition（P）,if ψ is 2-pure then Ysatisfies condition（P）,but the converse is not true.Some new generalizations of pure epimorphisms are given.Using these new concepts,some characterizations of condition（P′）and condition（PE）are obtained,that is,a S-act Ysatisfies condition（P′）,if and only if every S-epimorphism is weak 2-pure,and a S-act Y satisfies condition（PE）,if and only if every Sepimorphism is PE-2-pure.Finally,the directed colimits of these new epimorphisms are investigated.

关 键 词：纯满同态 条件(P′) 条件(PE) 

分 类 号：O153.3[理学—数学]