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Classification of Finite Rings of Order by Generators and Relations

Author

Listed:
  • P. Karimi Beiranvand
  • R. Beyranvand
  • M. Gholami

Abstract

For any finite abelian group , we define a binary operation or “multiplication†on and give necessary and sufficient conditions on this multiplication for to extend to a ring. Then we show when two rings made on the same group are isomorphic. In particular, it is shown that there are rings of order with characteristic , where is a prime number. Also, all finite rings of order are described by generators and relations. Finally, we give an algorithm for the computation of all finite rings based on their additive group.

Suggested Citation

  • P. Karimi Beiranvand & R. Beyranvand & M. Gholami, 2013. "Classification of Finite Rings of Order by Generators and Relations," Journal of Mathematics, Hindawi, vol. 2013, pages 1-8, January.
    • Handle: RePEc:hin:jjmath:467905
    DOI: 10.1155/2013/467905
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