The prime and maximal spectra and the reticulation of BL-algebras
Laurenťiu Leuštean
Open Mathematics, Tome 1 (2003), p. 382-397 / Harvested from The Polish Digital Mathematics Library
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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.

Publié le : 2003-01-01
EUDML-ID : urn:eudml:doc:268915 
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     author = {Lauren\v tiu Leu\v stean},
     title = {The prime and maximal spectra and the reticulation of BL-algebras},
     journal = {Open Mathematics},
     volume = {1},
     year = {2003},
     pages = {382-397},
     zbl = {1039.03052},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_BF02475217}
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Laurenťiu Leuštean. The prime and maximal spectra and the reticulation of BL-algebras. Open Mathematics, Tome 1 (2003) pp. 382-397. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_BF02475217/

[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] L.P. Belluce: “Semisimple algebras of infinite valued logic and bold fuzzy set theory”, Can. J. Math., Vol. 38, (1986), pp. 1356–1379. | Zbl 0625.03009

[3] L.P. Belluce: “Spectral spaces and non-commutative rings”, Comm. Algebra, Vol. 19, (1991), pp. 1855–1865. | Zbl 0728.16002

[4] W. Cornish: “Normal lattices”, J. Austral. Math. Soc., Vol. 14, (1972), pp. 200–215. | Zbl 0247.06009

[5] A. Di Nola, G. Georgescu, A. Iorgulescu: “Pseudo-BL algebras: Part I”, Mult.-Valued Log., Vol. 8, (2002), pp. 673–714. | Zbl 1028.06007

[6] A. Di Nola, G. Georgescu, A. Iorgulescu; “Pseudo-BL algebras: Part II”, Mult-Valued Log., Vol. 8, (2002), pp. 717–750. | Zbl 1028.06008

[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 | Zbl 0966.03055

[8] G. Georgescu: “The reticulation of a quantale”, Rev. Roum. Math. Pures Appl., Vol. 40, (1995), pp. 619–631. | Zbl 0858.06007

[9] G. Grätzer: Lattice Theory. First Concepts and Distributive Lattices, W.H. Freeman and Company, San Francisco, 1972.

[10] P. Hájek: Metamathematics of Fuzzy Logic, Trends in Logic-Studia Logica Library 4, Kluwer Academic Publishers, Dordrecht, 1998.

[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 | Zbl 0206.29701

[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] K.I. Rosenthal: Quantales and their applications, Longman Scientific and Technical, Longman House, Burnt Mill, 1989.

[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] E. Turunen: Mathematics behind fuzzy logic, Advances in Soft Computing, Physica-Verlag, Heidelberg, 1999. | Zbl 0940.03029

[16] E. Turunen: “BL-algebras of basic fuzzy logic”, Mathware Soft Comput., Vol. 6, (1999), pp. 49–61. | Zbl 0962.03020

[17] H. Wallman: “Lattices and topological spaces”, Ann. Math. (2), Vol. 39, (1938), pp. 112–126. http://dx.doi.org/10.2307/1968717 | Zbl 0018.33202