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

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

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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M. Abad, 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{M2006,
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 = {M. Abad, J. Díaz Varela, B. López Martinolich, M. C. Vannicola, M. Zander},
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 - M. Abad
AU - J. Díaz Varela
AU - B. López Martinolich
AU - M. C. Vannicola
AU - M. Zander
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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  1. [1] M. Abad: “Cyclic Post algebras of order n”, An. Acad. Brasil. Ciênc., Vol. 53(2), (1981), pp. 243–246. Zbl0473.06009
  2. [2] R. Balbes and P. Dwinger: Distributive Lattices, University of Missouri Press, Columbia, MO., 1974. 
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  8. [8] S. Lang: Algebra, Addison-Wesley Publishing Company, CA., 1984. 
  9. [9] R. Lewin: “Interpretability into Łukasiewicz algebras”, Rev. Un. Mat. Argentina, Vol. 41(3), (1999), pp. 81–98. Zbl0957.06012
  10. [10] R. McKenzie, G. McNulty and W. Taylor: Algebras, Lattices, Varieties, Vol. I, Wadsworth and Brooks, Monterey, CA, 1987. Zbl0611.08001
  11. [11] A. Monteiro: “Algèbres de Boole cycliques”, Rev. Roumaine de Mathématiques Pures Appl., Vol. 23(1), (1978), pp. 71–76. Zbl0393.06007
  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. Zbl0321.06013
  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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