Localization of LM n-algebras

Florentina Chirte§

Open Mathematics (2005)

  • Volume: 3, Issue: 1, page 105-124
  • ISSN: 2391-5455

Abstract

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The aim of this paper is to define the localization LM n-algebra of an LM n-algebra L with respect to a topology F on L; in Section 5 we prove that the maximal LM n-algebra of fractions (defined in [3]) and the LM n-algebra of fractions relative to an Λ-closed system (defined in Section 2) are LM n-algebras of localization.

How to cite

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Florentina Chirte§. "Localization of LM n-algebras." Open Mathematics 3.1 (2005): 105-124. <http://eudml.org/doc/268880>.

@article{FlorentinaChirte2005,
abstract = {The aim of this paper is to define the localization LM n-algebra of an LM n-algebra L with respect to a topology F on L; in Section 5 we prove that the maximal LM n-algebra of fractions (defined in [3]) and the LM n-algebra of fractions relative to an Λ-closed system (defined in Section 2) are LM n-algebras of localization.},
author = {Florentina Chirte§},
journal = {Open Mathematics},
keywords = {03D20; 06G30},
language = {eng},
number = {1},
pages = {105-124},
title = {Localization of LM n-algebras},
url = {http://eudml.org/doc/268880},
volume = {3},
year = {2005},
}

TY - JOUR
AU - Florentina Chirte§
TI - Localization of LM n-algebras
JO - Open Mathematics
PY - 2005
VL - 3
IS - 1
SP - 105
EP - 124
AB - The aim of this paper is to define the localization LM n-algebra of an LM n-algebra L with respect to a topology F on L; in Section 5 we prove that the maximal LM n-algebra of fractions (defined in [3]) and the LM n-algebra of fractions relative to an Λ-closed system (defined in Section 2) are LM n-algebras of localization.
LA - eng
KW - 03D20; 06G30
UR - http://eudml.org/doc/268880
ER -

References

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  1. [1] R. Balbes and Ph. Dwinger: Distributive Lattices, University of Missouri Press, 1974. 
  2. [2] V. Boicescu, A. Filipoiu, G. Georgescu and S. Rudeanu: Lukasiewicz-Moisil Algebras, North Holland, 1991. 
  3. [3] D. Buşneag and F. Chirteş: LM n -algebra of fractions and maximal LM n -algebra of fractions, to appear in Discrete Mathematics. 
  4. [4] D. Buşneag: “F-multipliers and the localization of Hilbert algebras”, Zeitschr. f. math. Logik und Grundlagen d. Math. Bd., Vol. 36, (1990), pp. 331–338. 
  5. [5] R. Cignoli: Algebras de Moisil, Notas de Logica Matematica, 27, Instituto de Matematica, Universidad del Sur, Bahia Blanca, 1970. Zbl0212.31701
  6. [6] R. Cignoli: “An algebraic approch to elementary theory based on n-valued Lukasiewicz logics”, Z. Math Logic u. Grund. Math., Vol. 30, (1984), pp. 87–96 http://dx.doi.org/10.1002/malq.19840300106 Zbl0551.03037
  7. [7] W.H. Cornish: “The multiplier extension of a distributive lattice”, Journal of Algebra, Vol. 32, (1974), pp. 339–355. http://dx.doi.org/10.1016/0021-8693(74)90143-4 
  8. [8] C. Dan: F-multipliers and the localization of Heyting algebras, Analele Universitâţii din Craiova, Seria Matematica-Informatica, Vol. XXIV, 1997, pp. 98–109. Zbl1053.03520
  9. [9] G. Georgescu and C. Vraciu: “On the Characterisation of Centred Lukasiewicz Algebras”, Journal of Algebra, Vol. 16(4), (1970), pp. 486–495. http://dx.doi.org/10.1016/0021-8693(70)90002-5 
  10. [10] G. Georgescu: “F-multipliers and localizations of distributive lattices”,Algebra Universalis,Vol 21, (1985),pp. 181–197. http://dx.doi.org/10.1007/BF01188055 Zbl0602.06006
  11. [11] J. Lambek: Lectures on Rings and Modules, Blaisdell Publishing Company, 1966. 
  12. [12] N. Popescu: Abelian categories with applications to rings and modules, Academic Press, New York, 1973. Zbl0271.18006
  13. [13] J. Schmid: “Multipliers on distributive lattices and rings of quotients”, Houston Journal of Mathematics, Vol. 6(3), (1980). Zbl0501.06008
  14. [14] J. Schmid: “Distributive lattices and rings of quotients”, Coll. Math. Societatis Janos Bolyai (Szeged, Hungary), Vol. 33, (1980). 
  15. [15] B. Strenström: “Platnes and localization over monoids”, Math. Nachrichten, Vol. 48, (1971), pp. 315–334. Zbl0199.33703

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