Conversion of Element Representations in Galois Rings

  • Juan Carlos Ku-CauichEmail author
  • Guillermo Morales-Luna


We are developing a symbolic calculator in order to computationally operate within Galois rings algebraic structure. In any Galois ring, whose characteristic is a power of a prime, each element has an additive representation, which is basically a remainder polynomial when dividing by a basic irreducible polynomial, and a p-adic representation given by Teichmüller elements, which are powers of roots of basic primitive polynomials. In this paper we introduce basic procedures to obtain Hensel’s lifts of primitive polynomials and the conversion between additive and p-adic representations.


Galois rings Teichmüller elements Symbolic computation 

Mathematics Subject Classification

13B05 13F20 12K99 



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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Juan Carlos Ku-Cauich
    • 1
    Email author
  • Guillermo Morales-Luna
    • 1
  1. 1.Computer Science, CINVESTAV-IPNMexico CityMexico

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