Resolution of Algebraic Systems of Equations in the Variety of Cyclic Post Algebras
There is a constructive method to define a structure of simple k-cyclic Post algebra of order p, Lp,k, on a given finite field F(pk), and conversely. There exists an interpretation Φ1 of the variety V(Lp,k) generated by Lp,k into the variety V(F(pk)) generated by F(pk) and an interpretation Φ2 of V(...
| Autores: | , |
|---|---|
| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2011 |
| País: | Argentina |
| Institución: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repositorio: | CONICET Digital (CONICET) |
| Idioma: | inglés |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/79693 |
| Acceso en línea: | http://hdl.handle.net/11336/79693 |
| Access Level: | acceso abierto |
| Palabra clave: | Equivalence Finite Fields GrÖBner Bases Post Algebras Varieties https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| Sumario: | There is a constructive method to define a structure of simple k-cyclic Post algebra of order p, Lp,k, on a given finite field F(pk), and conversely. There exists an interpretation Φ1 of the variety V(Lp,k) generated by Lp,k into the variety V(F(pk)) generated by F(pk) and an interpretation Φ2 of V(F(pk)) into V(Lp,k) such that Φ2Φ1(B) = B for every B ∈ V(Lp,k) and Φ1Φ2(R) = R for every R ∈ V(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. |
|---|