Compact representations of BL-algebras

Archive for Mathematical Logic

Volumn 42, Issue 8, 2003, Pages 737-761

  Di Nola, Antonio ^a   Leuştean, Laurenţiu ^b  

^a UNIVERSITY OF SALERNO   (Italy)

^b NATIONAL INSTITUTE FOR RESEARCH AND DEVELOPMENT IN INFORMATICS   (Romania)

Author keywords

Basic logic; BL algebras; Gelfand duality; Sheaf representations

Indexed keywords

EID: 0344982928     PISSN: 09335846     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00153-003-0178-y     Document Type: Article

References (26)

1. Bigard, A., Keimel, K., Wolfenstein, S.: Groupes et Anneaux Réticulés. Lect. Notes Math. 608, Springer Verlag, Berlin Heidelberg New York, 1977
2. Burris, S., Sankappanavar, H. P.: A Course in Universal Algebra, Springer Verlag, New York, 1981
3. Cignoli, R., D'Ottaviano, I.M.L., Mundici, D.: Algebraic Foundations of many-valued Reasoning. Kluwer Academic Publishers, Dordrecht, 2000
4. Cornish, W.: Normal lattices. J. Austral. Math. Soc., 14, 200-215 (1972)
5. Davey, B.A.: Sheaf spaces and sheaves of universal algebras. Math. Z. 134, 275-290 (1973)
6. Di Nola, A., Georgescu, G., Iorgulescu, A.: Pseudo-BL algebras I. Mult.-Valued Log. 134(5-6), 673-716 (2002)
7. Di Nola, A., Georgescu, G., Iorgulescu, A.: Pseudo-BL algebras II. Mult.-Valued Log. 134(5-6), 717-750 (2002)
8. Di Nola, A., Georgescu, G., Leuştean, L.: Boolean products of BL-algebras. J. Math. Anal. Appl. 251, 106-131 (2000)
9. Filipoiu, A., Georgescu, G.: Compact and Pierce representations of MV-algebras. Rev. Roum. Math. Pures Appl. 40(7-8), 599-618 (1995)
10. Gelfand, I., Kolmogoroff, A.: On rings of continuous functions on topological spaces. Dokl. Akad. Nauk. SSSR 22, 11-15 (1939)
11. Georgescu, G., Leuştean, L.: Some classes of pseudo-BL algebras. J. Austral. Math. Soc., 73, 127-153 (2002)
12. Georgescu, G., Voiculescu, I.: Some abstract maximal-ideal like spaces. Algebra Univers. 26(1-2), 90-102 (1989)
13. Hájek, P.: Metamathematics of Fuzzy Logic. Kluwer Academic Publishers, Dordrecht, 1998
14. Keimel, K.: The representation of lattice-ordered groups and rings by sections in sheaves. In: Lectures Appl. Sheaves Ring Theory. Tulane Univ. Ring Operator Theory Year 1970-1971, 3, Lect. Notes Math. 248, Springer Verlag, 1977, pp. 1-98
15. Leuştean, L.: The prime and maximal spectra and the reticulation of BL-algebras. Submitted
16. Mulvey, C.J.: Compact ringed spaces. J. Algebra 52, 411-436 (1978)
17. Mulvey, C.J.: Representations of rings and modules. In: Applications of sheaves. Proc. Res. Symp., Durham 1977, Lect. Notes Math. 753, Springer Verlag 1979, pp. 542-585
18. Mulvey, C.J.: A generalisation of Gelfand duality. J. Algebra 56, 499-505 (1979)
19. Pawar, Y.S.: Characterizations of normal lattices. Indian J. Pure Appl. Math. 24(11), 651-656 (1993)
20. Schubert, H.: Topology. Macdonald Technical and Scientific, London, 1968
21. Simmons, H.: Reticulated rings. J. Algebra 66, 169-192 (1980)
22. Swan, R.S.: The theory of sheaves. Chicago Lectures in Mathematics, The University of Chicago Press, Chicago and London, 1964
23. Tennison, B.R.: Sheaf theory. London Mathematical Society Lecture Notes Series 20, Cambridge University Press, Cambridge etc. 1975
24. Turunen, E.: BL-algebras of basic fuzzy logic, Mathware Soft Comput. 6(1), 49-61 (1999)
25. Turunen, E., Sessa, S.: Local BL-algebras. Mult.-Valued Log. 6(1-2), 229-249 (2001)
26. Wallman, H.: Lattices and topological spaces. Ann. Math. (2) 39, 112-126 (1938)