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EnglishBL-algebras were introduced by P. Hajek as algebraic structures of Basic Logic. The aim of the paper is a survey of 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, a class of finite BL-algebras, actually BL-comets, which can be seen as a generalization of finite BL-chain, is characterized. Then, just using BL-comets, any finite BL-algebra can be represented 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 finite MV-chains. Then it is shown the existence of a strong duality for each variety generated by one finite non-trivial totally ordered BL-algebra. As an application of the dualities, the injective and the weak injective members of these classes are described.
| Titolo: | Finiteness based results in BL-algebras | |
| Autori: | ||
| Data di pubblicazione: | 2005 | |
| Rivista: | ||
| Abstract: | BL-algebras were introduced by P. Hajek as algebraic structures of Basic Logic. The aim of the pa...per is a survey of 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, a class of finite BL-algebras, actually BL-comets, which can be seen as a generalization of finite BL-chain, is characterized. Then, just using BL-comets, any finite BL-algebra can be represented 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 finite MV-chains. Then it is shown the existence of a strong duality for each variety generated by one finite non-trivial totally ordered BL-algebra. As an application of the dualities, the injective and the weak injective members of these classes are described. | |
| Handle: | http://hdl.handle.net/11588/204566 | |
| Appare nelle tipologie: | 1.1 Articolo in rivista |
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