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

Studia Logica 98 (1-2):307-330 (2011)
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 Φ 1 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 Φ 2 of $${\mathcal{V}(F(p^k))}$$ into $${\mathcal{V}(L_{p,k})}$$ such that Φ 2 Φ 1 ( B ) = B for every $${B \in \mathcal{V}(L_{p,k})}$$ and Φ 1 Φ 2 ( 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.
Keywords Varieties  equivalence  finite fields  Post algebras  Gröbner bases
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DOI 10.1007/s11225-011-9330-6
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Raymond Balbes & Philip Dwinger (1977). Distributive Lattices. Journal of Symbolic Logic 42 (4):587-588.

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