AGP-内射环的奇异性  

Singularity of AGP-injective Rings

作　　者：董珺[1] 董长紫[2] 

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 [2]陇东学院数学系,甘肃庆阳745000

出　　处：《兰州工业高等专科学校学报》2006年第4期43-46,共4页Journal of Lanzhou Higher Polytechnical College

摘　　要：首先,研究了非奇异的AGP-内射环的正则性.证明了设R是右非奇异右AGP-内射环,如果R是右CF-环且每个主右理想都是双边理想,则R是正则环.其次,讨论了右AGP-内射环的非奇异性.证明了①右P-V′-环、右AGP-内射环是左非奇异的.②若R是右非奇异的,右有限Goldie维数的右AGP-内射环,则R是半单Artin的.最后,给出一个例子说明AGP-内射环和P-V′环均不具有左、右对称性.Firstly, the regularity of right nonsingular AGP - injective rings are studied. It is shown that let R be right nonsingular AGP- injeetive rings,if R be right CF rings and every right principal ideal is two - side ideal, then R is Von Neumann regular ring. Secondly, the nonsingularity of right AGP - injeetive rings are discussed. It is proved that ① Let R be right AGP - injeetive and right P - V＇ - ring, then R is left nonsingular ring. ②If R is right non - sin- gular, right AGP- injeetive and finite right Goldie dimensional,then R is artin semisimple ring. Finally, we give an example of left P - V＇ - ring, right AGP - injective ring but neither right P - V＇ - ring nor left AGP - injeetive ring.

关 键 词：AGP-内射环 Von Neumann正则环 非奇异环 P-V′-环 

分 类 号：O153.3[理学—数学]