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

top
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

top

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

top
  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
  6. [6] C.C. Chang: “Algebraic analysis of many valued logics”, Trans. Amer. Math. Soc., Vol. 88, (1958), pp. 467–490. http://dx.doi.org/10.2307/1993227 Zbl0084.00704
  7. [7] R. Cignoli, I.M.L. D'Ottaviano and D. Mundici: Algebraic foundation of many-valued Reasoning, Kluwer Academic Publishers, Dordrecht, 2000. 
  8. [8] 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 
  9. [9] W.H. Cornish: “A multiplier approach to implicative BCK-algebras”, Mathematics Seminar Notes, Kobe University, Vol. 8, No. 1, (1980), pp. 157–169. Zbl0465.03029
  10. [10] C. Dan: F-multipliers and the localisation of Heyting algebras, Analele Universitâţii din Craiova, Seria Matematica-Informatica, Vol. XXIV, 1997, pp. 98–109. 
  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
  12. [12] G. Georgescu and A. Iorgulescu: “Pseudo-MV algebras”, Multi. Val. Logic, Vol. 6, (2001), pp. 95–135. Zbl1014.06008
  13. [13] P. Hájek: Metamathematics of fuzzy logic Kluwer Acad. Publ., Dordrecht, 1998. 
  14. [14] J. Lambek: Lectures on Rings and Modules, Blaisdell Publishing Company, 1966. 
  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. 
  17. [17] J. Schmid: “Multipliers on distributive lattices and rings of quotients”, Houston Journal of Mathematics, Vol. 6, No. 3, (1980), pp. 401–425. Zbl0501.06008
  18. [18] J. Schmid: Distributive lattices and rings of quotients, Coll. Math. Societatis Janos Bolyai, Szeged, Hungary, 1980. Zbl0501.06008

NotesEmbed ?

top

You must be logged in to post comments.