本文選題：單位正則元 + 特殊clean元�。� 參考：《數(shù)學(xué)進展》2017年04期

【摘要】：環(huán)R稱為可分環(huán),如果對任何有限生成投射右R-模A和B,A崴A≌A崴B≌B崴B崴A≌B.假設(shè)R是置換可分環(huán),其中2可逆,a-a~3∈R正則,證明了a∈R單位正則當且僅當R(1-a~2)R=Rr(a)=e(a)R.環(huán)R中元素a稱為特殊clean元,如果有冪等元e∈R使得a-e∈R可逆,而且aR∩eR=0.進一步,證明了a∈R是特殊clean元,如果aR/ar(a~2),R/(aR+r(a))投射,而且R(a-a~3)R=Rar(a~2)=e(a~2)aR.由此推廣了正則可分環(huán)中相關(guān)結(jié)論.
[Abstract]:A ring R is called a separable ring, if the right R module A and B A Wok A are projected to any finitely generated R module A and B = A Wei B = B Wei B Wei A = B = B = B = B = B = B = B = B = B = B = B Assuming that R is permutation separable ring, where 2 invertible a-a ~ + 3 鈭，

本文編號：1833788