外强素根(英文)  

The external strongly prime radical

作　　者：于淑兰[1] 张宪君 

机构地区：[1]山东大学威海分校数学与统计学院,威海264209 [2]哈尔滨工业大学(威海)数学系,威海264209

出　　处：《黑龙江大学自然科学学报》2012年第2期149-151,159,共4页Journal of Natural Science of Heilongjiang University

摘　　要：定义外强素环,即一个环R的每个非零理想包含一个有限子集G,使得由rGr=0,r∈R可推出r=0。所有外强素环组成的环类所确定的上根称为外强素根。证明下列主要结论:A.外强素环一定是右(左)强素环;B.外强素环的每个非零理想也是外强素环;C.外强素环类本质扩张闭的;D.设(S,W,V,T)是一个Morita-Context且VW=S,WV=T,其中S,T是两个有1的环,如果I是S的一个理想,使得S/I是外强素环,那么T/J也是外强素环,其中J=WIV。A ring R are called an external strongly prime ring,if every non-zero idea of R contains a finite subset G,such that rGr=0,r∈R,implies r=0.Upper radical determined by the class of all the external strongly prime rings is called the external strongly prime radical.It is shown that：A.An external strongly prime ring is right（left） strongly prime ring;B.Any non-zero ideal of external strongly prime rings is an external strongly prime ring;C.The essential extensions of the class of external strongly prime rings are again external strongly prime rings;D.Let（S,V,W,T） be a Morita-context with VW=S,WV=T,where S and T are rings with 1,if I is an ideal of S,such that S/I is an external strongly prime ring,then T/J is also an external strongly prime ring,where J=WIV.

关 键 词：外强素环 右强素环 外强素根 

分 类 号：O153.3[理学—数学]