An equivalence between varieties of cyclic Post algebras and varieties generated by a finite field

Abad Manuel; Díaz Varela J.; López Martinolich B.; C. Vannicola M.; Zander M.

Open Mathematics (2006)

  • Volume: 4, Issue: 4, page 547-561
  • ISSN: 2391-5455

Abstract

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In this paper we give a term equivalence between the simple k-cyclic Post algebra of order p, L p,k, and the finite field F(p k) with constants F(p). By using Lagrange polynomials, we give an explicit procedure to obtain an interpretation Φ1 of the variety V(L p,k) generated by L p,k into the variety V(F(p k)) generated by F(p k) and an interpretation Φ2 of V(F(p k)) into V(L p,k) such that Φ2Φ1(B) = B for every B ε V(L p,k) and Φ1Φ2(R) = R for every R ε V(F(p k)).

How to cite

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Abad Manuel, et al. "An equivalence between varieties of cyclic Post algebras and varieties generated by a finite field." Open Mathematics 4.4 (2006): 547-561. <http://eudml.org/doc/268989>.

@article{AbadManuel2006,
abstract = {In this paper we give a term equivalence between the simple k-cyclic Post algebra of order p, L p,k, and the finite field F(p k) with constants F(p). By using Lagrange polynomials, we give an explicit procedure to obtain an interpretation Φ1 of the variety V(L p,k) generated by L p,k into the variety V(F(p k)) generated by F(p k) and an interpretation Φ2 of V(F(p k)) into V(L p,k) such that Φ2Φ1(B) = B for every B ε V(L p,k) and Φ1Φ2(R) = R for every R ε V(F(p k)).},
author = {Abad Manuel, Díaz Varela J., López Martinolich B., C. Vannicola M., Zander M.},
journal = {Open Mathematics},
keywords = {06D25; 12E20; 03G25},
language = {eng},
number = {4},
pages = {547-561},
title = {An equivalence between varieties of cyclic Post algebras and varieties generated by a finite field},
url = {http://eudml.org/doc/268989},
volume = {4},
year = {2006},
}

TY - JOUR
AU - Abad Manuel
AU - Díaz Varela J.
AU - López Martinolich B.
AU - C. Vannicola M.
AU - Zander M.
TI - An equivalence between varieties of cyclic Post algebras and varieties generated by a finite field
JO - Open Mathematics
PY - 2006
VL - 4
IS - 4
SP - 547
EP - 561
AB - In this paper we give a term equivalence between the simple k-cyclic Post algebra of order p, L p,k, and the finite field F(p k) with constants F(p). By using Lagrange polynomials, we give an explicit procedure to obtain an interpretation Φ1 of the variety V(L p,k) generated by L p,k into the variety V(F(p k)) generated by F(p k) and an interpretation Φ2 of V(F(p k)) into V(L p,k) such that Φ2Φ1(B) = B for every B ε V(L p,k) and Φ1Φ2(R) = R for every R ε V(F(p k)).
LA - eng
KW - 06D25; 12E20; 03G25
UR - http://eudml.org/doc/268989
ER -

References

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  7. [7] K. Kaarly and A.F. Pixley: Polynomial Completeness in Algebraic Systems, Chapman and Hall, Boca Raton, 2001.  
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  10. [10] R. McKenzie, G. McNulty and W. Taylor: Algebras, Lattices, Varieties, Vol. I, Wadsworth and Brooks, Monterey, CA, 1987.  
  11. [11] A. Monteiro: “Algèbres de Boole cycliques”, Rev. Roumaine de Mathématiques Pures Appl., Vol. 23(1), (1978), pp. 71–76.  
  12. [12] G. Moisil: Algebra schemelor cu elemente ventil, Seria St. nat. 4–5, Revista Universitatii C.I. Parhon, Bucharest, 1954, pp. 9–15.  
  13. [13] G. Moisil: “Algèbres universelles et automates”, In: Essais sur les Logiques non Chrysippiennes, Editions de L’Academie de la Republique Socialiste de Roumanie, Bucharest, 1972.  
  14. [14] S. Rudeanu: Boolean functions and equations, North-Holland Publishing Co., Amsterdam-London; American Elsevier Publishing Co., Inc., New York, 1974.  
  15. [15] M. Serfati: “Introduction aux Algèbres de Post et à leurs applications (logiques à r valeurs-équations postiennes-graphoïdes orientés)”, Cahiers du Bureau Universitaire de Recherche Opérationnelle Université Paris VI. Série Recherche, Vol. 21, (1973), pp. 35–42.  

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