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One Commutativity Condition of Jacobson Semi-Simple Ring

Conference paper
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 223)

Abstract

The study of ring commutativity was beneficial for discussion of some properties about rings. At the same time, commutative rings were studied in Commutative Algebra. To study some important properties on rings, study of commutativity of rings became more and more important. He used some methods and theorems from the literature on the central element, and then gave some proof about semi-prime ring commutativity conditions. When R is the division ring or R is J-semi simple ring, he hierarchically certificate that ring is commutativity, given the final conclusions, other conclusions can be proof similarly. It is the promotion of some conclusions, by weakening conditions; it had a broader range of applications.

Keywords

Semi-prime ring Non-zero divisor Commutativity 

Notes

Acknowledgments

I appreciate the assistance and encouragement of my teachers and colleagues, in the process of thesis writing. As a teacher, I deeply feel that the knowledge is an ocean and I will continue to explore and learn. Hope to go further in this piece of Knowledge Ocean. The articles of many teachers gave me a lot of help, and they provided me with many good ideas, so I am grateful to the teachers who pay hard work in the process of the ring exchange theory.

References

  1. 1.
    Zhu J, Yv XJ (2003) Semi simple rings commutatively conditions. In: J Harbin Norm Univ Nat Sci (19)3:9–10Google Scholar
  2. 2.
    Zhu J, Yv XJ (1998) Central element of semi prime ring and exchange. In: J Heilongjiang Univ Nat Sci 7(3):28–30Google Scholar
  3. 3.
    Guo YC (1991) Central element of semi prime ring. J Jilin Univ Nat Sci 9(1):33–36Google Scholar
  4. 4.
    Herstein I (1955) Tow remarks on the commutability of rings. Canada 3(4):411–412Google Scholar
  5. 5.
    Yu WD, Zhang HY, Yang XS (2009) Commutability of semi-prime rings with variable identity. J Harbin Norm Univ Nat Sci 5(5):13–15Google Scholar
  6. 6.
    Bai H, Yang XS, Chen GH, Du JH (2009) Commutativity of rings with variable identity. J Harbin Univ Sci Technol 114(16):23–25Google Scholar
  7. 7.
    Zhang HY, Yu WD, Yang XS (2011) A generalization on the commutativity conditions of semiprime-PI rings. J Harbin Univ Sci Technol 3(6):28–30Google Scholar
  8. 8.
    Bell HE, Yaqub A (2009) On commutativity of semi periodic rings. Result Math 53(3):19–26Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Department of MathematicsHeilongjiang Institute of TechnologyHarbinChina
  2. 2.Department of MathematicsHarbin University of Science and TechnologyHarbinChina

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