论文信息 - Compact Representations of BL-Algebras

Compact Representations of BL-Algebras

In this paper we define sheaf spaces of BL-algebras (or BL-sheaf spaces), we study completely regular and compact BL-sheaf spaces and compact representations of BL-algebras and, finally, we prove that the category of non-trivial BL-algebras is equivalent with the category of compact local BL-sheaf spaces.

Antonio Di Nola | A. Nola | Laurentiu Leustean | Laurenţiu Leuştean

[1] Ioana Voiculescu,et al. Some abstract maximal ideal-like spaces , 1989 .

[2] Stanley Burris,et al. A course in universal algebra , 1981, Graduate texts in mathematics.

[3] George Georgescu,et al. Some classes of pseudo-BL algebras , 2002, Journal of the Australian Mathematical Society.

[4] E. Turunen. BL-algebras of basic fuzzy logic , 1999 .

[5] A. Nola,et al. Boolean products of BL-algebras , 2000 .

[6] Christopher J. Mulvey,et al. Compact ringed spaces , 1978 .

[7] D. B. A. Epstein. The Theory of Sheaves. By Richard G. Swan. Chicago lectures in mathematics. (University of Chicago Press) , 1966 .

[8] On Rings of Continuous Functions on Topological Spaces , 1993 .

[9] D. Mundici,et al. Algebraic Foundations of Many-Valued Reasoning , 1999 .

[10] Laurentiu Leustean,et al. The prime and maximal spectra and the reticulation of BL-algebras , 2003 .

[11] Christopher J. Mulvey,et al. Representations of rings and modules , 1979 .

[12] Brian A. Davey,et al. Sheaf spaces and sheaves of universal algebras , 1973 .

[13] H. Wallman,et al. Lattices and Topological Spaces , 1938 .

[14] Christopher J. Mulvey,et al. A generalisation of Gelfand duality , 1979 .

[15] Petr Hájek,et al. Metamathematics of Fuzzy Logic , 1998, Trends in Logic.

[16] Klaus Keimel,et al. Groupes et anneaux réticulés , 1977 .