INMABB   05456
INSTITUTO DE MATEMATICA BAHIA BLANCA
Unidad Ejecutora - UE
artículos
Título:
Resolution of Algebraic system of Equations in the varity of Cyclic Algebras
Autor/es:
DÍAZ VARELA, JOSÉ PATRICIO ; LÓPEZ MARTINOLICH, BLANCA FERNANDA
Revista:
STUDIA LOGICA
Editorial:
Springer
Referencias:
Año: 2011 vol. 98 p. 307 - 330
ISSN:
0039-3215
Resumen:
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 $Phi_1$ of the variety ${cal V}(L_{p,k})$ generated by $L_{p,k}$ into the variety ${cal V}(F(p^k))$ generated by $F(p^k)$ and an interpretation $Phi_2$ of ${cal V}(F(p^k))$ into ${cal V}(L_{p,k}$) such that  $Phi_2$$Phi_1(B)=B$ for every $B in {cal V}(L_{p,k}$) and $Phi_1 Phi_2(R)=R$ for every $R in {cal V}(F(p^k))$. In this paper we show how we could solve an algebraic system of equations over an arbitrary cyclic Post algebra of order $p$, $p$ prime, using the above interpretation, Gr"obner bases and algorithms programmed in Maple.