论文标题
强烈交换戒指
Strongly exchange rings
论文作者
论文摘要
两个Elements $ a，b $ in Ring $ r $形成一个正确的副本对，书面$ \ langle a，b \ rangle $，如果$ ar+ar+br = r $。右副作用对已显示在左转或交换环的研究中非常有用。在本文中，我们根据其下降的链条定义了强烈的交换环类。我们证明它们是半牙的，并且这类环包含左下角，左纯净的，左下角，局部和左连续环。这使我们能够根据右副作用对下降链的行为对所有这些类别的戒指进行统一的研究。
Two elements $a,b$ in a ring $R$ form a right coprime pair, written $\langle a,b\rangle$, if $aR+bR=R$. Right coprime pairs have shown to be quite useful in the study of left cotorsion or exchange rings. In this paper, we define the class of strongly right exchange rings in terms of descending chains of them. We show that they are semiregular and that this class of rings contains left injective, left pure-injective, left cotorsion, local and left continuous rings. This allows us to give a unified study of all these classes of rings in terms of the behaviour of descending chains of right coprime pairs.
