Pseudo-MV algebra of fractions and maximal pseudo-MV algebra of quotients

Dana Piciu

Open Mathematics (2004)

  • Volume: 2, Issue: 2, page 199-217
  • ISSN: 2391-5455

Abstract

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The aim of this paper is to define the notions of pseudo-MV algebra of fractions and maximal pseudo-MV algebra of quotients for a pseudo-MV algebra (taking as a guide-line the elegant construction of complete ring of quotients by partial morphisms introduced by G. Findlay and J. Lambek-see [14], p.36). For some informal explanations of the notion of fraction see [14], p. 37. In the last part of this paper the existence of the maximal pseudo-MV algebra of quotients for a pseudo-MV algebra (Theorem 4.5) is proven and I give explicit descriptions of this MV-algebra for some classes of pseudo MV-algebras.

How to cite

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Dana Piciu. "Pseudo-MV algebra of fractions and maximal pseudo-MV algebra of quotients." Open Mathematics 2.2 (2004): 199-217. <http://eudml.org/doc/268710>.

@article{DanaPiciu2004,
abstract = {The aim of this paper is to define the notions of pseudo-MV algebra of fractions and maximal pseudo-MV algebra of quotients for a pseudo-MV algebra (taking as a guide-line the elegant construction of complete ring of quotients by partial morphisms introduced by G. Findlay and J. Lambek-see [14], p.36). For some informal explanations of the notion of fraction see [14], p. 37. In the last part of this paper the existence of the maximal pseudo-MV algebra of quotients for a pseudo-MV algebra (Theorem 4.5) is proven and I give explicit descriptions of this MV-algebra for some classes of pseudo MV-algebras.},
author = {Dana Piciu},
journal = {Open Mathematics},
keywords = {06D35; 03G25},
language = {eng},
number = {2},
pages = {199-217},
title = {Pseudo-MV algebra of fractions and maximal pseudo-MV algebra of quotients},
url = {http://eudml.org/doc/268710},
volume = {2},
year = {2004},
}

TY - JOUR
AU - Dana Piciu
TI - Pseudo-MV algebra of fractions and maximal pseudo-MV algebra of quotients
JO - Open Mathematics
PY - 2004
VL - 2
IS - 2
SP - 199
EP - 217
AB - The aim of this paper is to define the notions of pseudo-MV algebra of fractions and maximal pseudo-MV algebra of quotients for a pseudo-MV algebra (taking as a guide-line the elegant construction of complete ring of quotients by partial morphisms introduced by G. Findlay and J. Lambek-see [14], p.36). For some informal explanations of the notion of fraction see [14], p. 37. In the last part of this paper the existence of the maximal pseudo-MV algebra of quotients for a pseudo-MV algebra (Theorem 4.5) is proven and I give explicit descriptions of this MV-algebra for some classes of pseudo MV-algebras.
LA - eng
KW - 06D35; 03G25
UR - http://eudml.org/doc/268710
ER -

References

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  1. [1] D. Buşneag: “Hilbert algebra of fractions and maximal Hilbert algebras of quotients”, Kobe Journal of Mathematics, Vol. 5, (1988), pp. 161–172. Zbl0676.06018
  2. [2] D. Buşneag and D. Piciu: Meet-irreducible ideals in an MV-algebra, Analele Universitâţii din Craiova, Seria Matematica-Informatica, Vol. XXVIII, 2001, pp. 110–119. Zbl1058.06014
  3. [3] D. Buşneag and D. Piciu: “On the lattice of ideals of an MV-algebra”, Scientiae Mathematicae Japonicae, Vol. 56, No. 2, (2002), pp. 367–372, e6, pp. 221–226. Zbl1019.06004
  4. [4] D. Buşneag and D. Piciu: MV-algebra of fractions relative to an λ-closed system, Analele Universitâţii din Craiova, Seria Matematica-Informatica, Vol. XXX, 2003, pp. 1–6. Zbl1073.06501
  5. [5] D. Buşneag and D. Piciu: “MV-algebra of fractions and maximal MV-algebra of quotients”, to appear in Journal of Multiple-Valued Logic and Soft Computing. Zbl1069.06006
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  11. [11] A. Dvurečenskij: “Pseudo-MV-algebras are intervals in l-groups”, Journal of Australian Mathematical Society, Vol. 72, (2002), pp. 427–445. http://dx.doi.org/10.1017/S1446788700036806 Zbl1027.06014
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  15. [15] I. Leuştean: “Local Pseudo-MV algebras”, Soft Computing, Vol. 5, (2001), pp. 386–395. http://dx.doi.org/10.1007/s005000100141 Zbl0992.06011
  16. [16] D. Piciu: Pseudo-MV algebra of fractions relative to an λ-closed system, Analele Universitâţii din Craiova, Seria Matematica-Informatica, Vol. XXX, 2003, pp. 7–13. 
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  18. [18] J. Schmid: Distributive lattices and rings of quotients, Coll. Math. Societatis Janos Bolyai, Szeged, Hungary, 1980. Zbl0501.06008

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