JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2021, Vol. 56 ›› Issue (12): 67-71.doi: 10.6040/j.issn.1671-9352.0.2021.192

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Jordan and Lie centralizers on quaternion rings

CAO Mei-hong, ZHANG Jian-hua*   

  1. School of Mathematics and Statistics, Shaanxi Normal University, Xian 710119, Shaanxi, China
  • Published:2021-11-25

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Abstract: 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 φ on H(S) is centralizer.

Key words: quaternion ring, Jordan centralizer, Lie centralizer

CLC Number: 

  • O177.1
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