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

Open Mathematics (2003)

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

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topLaurenťiu 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] 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. Zbl0625.03009
- [3] L.P. Belluce: “Spectral spaces and non-commutative rings”, Comm. Algebra, Vol. 19, (1991), pp. 1855–1865. Zbl0728.16002
- [4] W. Cornish: “Normal lattices”, J. Austral. Math. Soc., Vol. 14, (1972), pp. 200–215. Zbl0247.06009
- [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] A. Di Nola, G. Georgescu, A. Iorgulescu; “Pseudo-BL algebras: Part II”, Mult-Valued Log., Vol. 8, (2002), pp. 717–750. Zbl1028.06008
- [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 Zbl0966.03055
- [8] G. Georgescu: “The reticulation of a quantale”, Rev. Roum. Math. Pures Appl., Vol. 40, (1995), pp. 619–631. Zbl0858.06007
- [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 Zbl0206.29701
- [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. Zbl0940.03029
- [16] E. Turunen: “BL-algebras of basic fuzzy logic”, Mathware Soft Comput., Vol. 6, (1999), pp. 49–61. Zbl0962.03020
- [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

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