|Title||Resolution of algebraic systems of equations in the variety of cyclic Post algebras.|
|Author(s)|| B.F. Lopez Martinolich, J.P. Diaz Varela|
|Type||Article in Journal|
|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 (Lp,k) generated by L p,k into the variety (F(pk)) generated by F(p k ) and an interpretation Φ2 of (F(pk)) into (Lp,k) such that Φ2Φ1(B) = B for every B∈(Lp,k) and Φ1Φ2(R) = R for every R∈(F(pk)).|
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|
|Publisher||Springer Netherlands, Dordrecht; Polish Academy of Sciences, Institute of Philosophy and Sociology, |