四元数环上的Jordan和Lie中心化子

Jordan and Lie centralizers on quaternion rings

设S是环,H(S)是S上的四元数环。通过研究H(S)上的Jordan中心化子和Lie中心化子,得到Lie中心化子是标准型的充分条件,证明在某特定假设下,H(S)上的每个Jordan中心化子是中心化子。此外,给出H(S)上的可加映射?是中心化子的几个等价条件。

Let S be a ring, H(S) be the quaternion ring on S. By studying Jordan centralizers and Lie centralizers on H(S), this paper obtains the sufficient condition for a centralizer to be proper. Further it’s proved that every Jordan centralizer is a centralizer on H(S) under certain assumption. Moreover, several equivalent conditions are given that the addictive mapping ? on H(S) is centralizer.