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.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.