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2003 | 1 | 3 | 382-397
Tytuł artykułu

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

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Wydawca
Czasopismo
Rocznik
Tom
1
Numer
3
Strony
382-397
Opis fizyczny
Daty
wydano
2003-09-01
online
2003-09-01
Twórcy
  • National Institute for Research and Development in Informatics, leo@u3.ici.ro
Bibliografia
  • [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.
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  • [4] W. Cornish: “Normal lattices”, J. Austral. Math. Soc., Vol. 14, (1972), pp. 200–215.
  • [5] A. Di Nola, G. Georgescu, A. Iorgulescu: “Pseudo-BL algebras: Part I”, Mult.-Valued Log., Vol. 8, (2002), pp. 673–714.
  • [6] A. Di Nola, G. Georgescu, A. Iorgulescu; “Pseudo-BL algebras: Part II”, Mult-Valued Log., Vol. 8, (2002), pp. 717–750.
  • [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
  • [8] G. Georgescu: “The reticulation of a quantale”, Rev. Roum. Math. Pures Appl., Vol. 40, (1995), pp. 619–631.
  • [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
  • [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.
  • [16] E. Turunen: “BL-algebras of basic fuzzy logic”, Mathware Soft Comput., Vol. 6, (1999), pp. 49–61.
  • [17] H. Wallman: “Lattices and topological spaces”, Ann. Math. (2), Vol. 39, (1938), pp. 112–126. http://dx.doi.org/10.2307/1968717
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_BF02475217
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