QF的刻划(英文)  

A CHARACTERIZATION OF QF RINGS

作　　者：董珺[1] 魏杰[1] 

机构地区：[1]兰州工业高等专科学校基础学科部,甘肃兰州730050

出　　处：《兰州工业高等专科学校学报》2007年第3期1-3,共3页Journal of Lanzhou Higher Polytechnical College

摘　　要：研究了关于右零化子满足升链和降链条件的环,即Artinian环和Noether环.设R是左P-内射环且非零补左理想在R中不小,若R满足条件(*),则R是右Artinian环.证明了R是QF环当且仅当R是满足条件(*)的左2-内射环且非零补左理想在R中不小.In this paper, the Artinian and Noethrian rings are studied with ascending and descending chain conditions on right ideals. Let R be a left P - injective ring so that each non - zero complement left ideal is not small,it shows that if R satisfies （ ＊ ）, then R is right Artinian. We also prove that R is QF if and only if R is left 2 - injective with satisfying（ ＊ ）, and every non - zero complement left ideal is not small.

关 键 词：Artinian环 NOETHER环 QF环 

分 类 号：O153.3[理学—数学]