Conversion of Element Representations in Galois Rings
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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.
KeywordsGalois rings Teichmüller elements Symbolic computation
Mathematics Subject Classification13B05 13F20 12K99
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