黑龙江大学自然科学学报
黑龍江大學自然科學學報
흑룡강대학자연과학학보
JOURNAL OF NATURAL SCIENCE OF HEILONGJIANG UNIVERSITY
2012年
2期
149-151,159
,共4页
外强素环%右强素环%外强素根
外彊素環%右彊素環%外彊素根
외강소배%우강소배%외강소근
external strongly prime ring%right strongly prime ring%external strongly prime radical
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.
定義外彊素環,即一箇環R的每箇非零理想包含一箇有限子集G,使得由rGr=0,r∈R可推齣r=0.所有外彊素環組成的環類所確定的上根稱為外彊素根.證明下列主要結論:A.外彊素環一定是右(左)彊素環；B.外彊素環的每箇非零理想也是外彊素環；C.外彊素環類本質擴張閉的；D.設(S,W,V,T)是一箇Morita - Context且VW=S,WV=T,其中S,T是兩箇有1的環,如果I是S的一箇理想,使得S/I是外彊素環,那麽T/J也是外彊素環,其中J=WIV.
정의외강소배,즉일개배R적매개비령이상포함일개유한자집G,사득유rGr=0,r∈R가추출r=0.소유외강소배조성적배류소학정적상근칭위외강소근.증명하렬주요결론:A.외강소배일정시우(좌)강소배；B.외강소배적매개비령이상야시외강소배；C.외강소배류본질확장폐적；D.설(S,W,V,T)시일개Morita - Context차VW=S,WV=T,기중S,T시량개유1적배,여과I시S적일개이상,사득S/I시외강소배,나요T/J야시외강소배,기중J=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.
