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Resolution of Algebraic Systems of Equations in the Variety of Cyclic Post Algebras

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Abstract

There is a constructive method to define a structure of simple k-cyclic Post algebra of order p, L p,k , on a given finite field F(p k), and conversely. There exists an interpretation Φ1 of the variety \({\mathcal{V}(L_{p,k})}\) generated by L p,k into the variety \({\mathcal{V}(F(p^k))}\) generated by F(p k) and an interpretation Φ2 of \({\mathcal{V}(F(p^k))}\) into \({\mathcal{V}(L_{p,k})}\) such that Φ2Φ1(B) =  B for every \({B \in \mathcal{V}(L_{p,k})}\) and Φ1Φ2(R) =  R for every \({R \in \mathcal{V}(F(p^k))}\).

In this paper we show how we can solve an algebraic system of equations over an arbitrary cyclic Post algebra of order p, p prime, using the above interpretation, Gröbner bases and algorithms programmed in Maple.

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Correspondence to B. F. López Martinolich.

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Díaz Varela, J.P., López Martinolich, B.F. Resolution of Algebraic Systems of Equations in the Variety of Cyclic Post Algebras. Stud Logica 98, 307–330 (2011). https://doi.org/10.1007/s11225-011-9330-6

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Keywords

  • Varieties
  • equivalence
  • finite fields
  • Post algebras
  • Gröbner bases