Finiteness based results in BL-algebras |
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Authors: | A D Nola A Lettieri |
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Affiliation: | (1) Dipartimento di Matematica e Informatica, Università di Salerno, Via S. Allende, Baronissi (Salerno);(2) Dipartimento di Costruzioni e Metodi Matematici in Architettura, Università di Napoli Federico II, via Monteoliveto 3, 80134 Napoli, Italy |
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Abstract: | BL-algebras were introduced by P. Hájek as algebraic structures of Basic Logic. The aim of this paper is to survey known results
about the structure of finite BL-algebras and natural dualities for varieties of BL-algebras. Extending the notion of ordinal sum of BL-algebras , we characterize a class of finite BL-algebras, actually BL-comets, which can be seen as a generalization of finite BL-chains. Then, just using BL-comets, we can represent any finite BL-algebra A as a direct product of BL-comets. This result can be seen as a generalization of the representation of finite MV-algebras as a direct product of MV-chains. Then we consider the varieties generated by one finite non-trivial totally ordered BL-algebra. For each of these varieties, we show the existence of a strong duality. As an application of the dualities, the
injective and the weak injective members of these classes are described. |
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Keywords: | BL-algebra BL-comet Duality Strong duality |
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