The prime and maximal spectra and the reticulation of BL-algebras

Laurenťiu Leuštean

Open Mathematics (2003)

  • Volume: 1, Issue: 3, page 382-397
  • ISSN: 2391-5455

Abstract

top
In this paper we study the prime and maximal spectra of a BL-algebra, proving that the prime spectrum is a compact T 0 topological space and that the maximal spectrum is a compact Hausdorff topological space. We also define and study the reticulation of a BL-algebra.

How to cite

top

Laurenťiu Leuštean. "The prime and maximal spectra and the reticulation of BL-algebras." Open Mathematics 1.3 (2003): 382-397. <http://eudml.org/doc/268915>.

@article{LaurenťiuLeuštean2003,
abstract = {In this paper we study the prime and maximal spectra of a BL-algebra, proving that the prime spectrum is a compact T 0 topological space and that the maximal spectrum is a compact Hausdorff topological space. We also define and study the reticulation of a BL-algebra.},
author = {Laurenťiu Leuštean},
journal = {Open Mathematics},
keywords = {08A72; 03G25; 06F99; 06D05},
language = {eng},
number = {3},
pages = {382-397},
title = {The prime and maximal spectra and the reticulation of BL-algebras},
url = {http://eudml.org/doc/268915},
volume = {1},
year = {2003},
}

TY - JOUR
AU - Laurenťiu Leuštean
TI - The prime and maximal spectra and the reticulation of BL-algebras
JO - Open Mathematics
PY - 2003
VL - 1
IS - 3
SP - 382
EP - 397
AB - In this paper we study the prime and maximal spectra of a BL-algebra, proving that the prime spectrum is a compact T 0 topological space and that the maximal spectrum is a compact Hausdorff topological space. We also define and study the reticulation of a BL-algebra.
LA - eng
KW - 08A72; 03G25; 06F99; 06D05
UR - http://eudml.org/doc/268915
ER -

References

top
  1. [1] M.F. Atiyah and I.G. Macdonald: Introduction to Commutative Algebra, Addison-Wesley Publishing Company, Reading, Massachussets, Menlo Park, California-London-Don Mills, Ontario, 1969. 
  2. [2] L.P. Belluce: “Semisimple algebras of infinite valued logic and bold fuzzy set theory”, Can. J. Math., Vol. 38, (1986), pp. 1356–1379. Zbl0625.03009
  3. [3] L.P. Belluce: “Spectral spaces and non-commutative rings”, Comm. Algebra, Vol. 19, (1991), pp. 1855–1865. Zbl0728.16002
  4. [4] W. Cornish: “Normal lattices”, J. Austral. Math. Soc., Vol. 14, (1972), pp. 200–215. Zbl0247.06009
  5. [5] A. Di Nola, G. Georgescu, A. Iorgulescu: “Pseudo-BL algebras: Part I”, Mult.-Valued Log., Vol. 8, (2002), pp. 673–714. Zbl1028.06007
  6. [6] A. Di Nola, G. Georgescu, A. Iorgulescu; “Pseudo-BL algebras: Part II”, Mult-Valued Log., Vol. 8, (2002), pp. 717–750. Zbl1028.06008
  7. [7] A. Di Nola, G. Georgescu, L. Leuštean: “Boolean products of BL-algebras”, J. Math. Anal. Appl., Vol. 251, (2000), pp. 106–131. http://dx.doi.org/10.1006/jmaa.2000.7024 Zbl0966.03055
  8. [8] G. Georgescu: “The reticulation of a quantale”, Rev. Roum. Math. Pures Appl., Vol. 40, (1995), pp. 619–631. Zbl0858.06007
  9. [9] G. Grätzer: Lattice Theory. First Concepts and Distributive Lattices, W.H. Freeman and Company, San Francisco, 1972. 
  10. [10] P. Hájek: Metamathematics of Fuzzy Logic, Trends in Logic-Studia Logica Library 4, Kluwer Academic Publishers, Dordrecht, 1998. 
  11. [11] M. Mandelker: “Relative annihilators in lattices”, Duke Math. J., Vol. 37, (1970), pp. 377–386. http://dx.doi.org/10.1215/S0012-7094-70-03748-8 Zbl0206.29701
  12. [12] A. Monteiro and L’arithm: “etique des filtres et les espaces topologiques. I–II”, Notas de Lógica Mathématica, No. 29-30, Instituto de Mathématica, Univ. Nac. del Sur. Bahia Blanca, Argentina, 1974. 
  13. [13] K.I. Rosenthal: Quantales and their applications, Longman Scientific and Technical, Longman House, Burnt Mill, 1989. 
  14. [14] H. Simmons: “Reticulated rings”, J. Algebra, Vol. 66, (1980), pp. 169–192. http://dx.doi.org/10.1016/0021-8693(80)90118-0 
  15. [15] E. Turunen: Mathematics behind fuzzy logic, Advances in Soft Computing, Physica-Verlag, Heidelberg, 1999. Zbl0940.03029
  16. [16] E. Turunen: “BL-algebras of basic fuzzy logic”, Mathware Soft Comput., Vol. 6, (1999), pp. 49–61. Zbl0962.03020
  17. [17] H. Wallman: “Lattices and topological spaces”, Ann. Math. (2), Vol. 39, (1938), pp. 112–126. http://dx.doi.org/10.2307/1968717 Zbl0018.33202

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.