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Boolean representation of bounded BCK-algebras

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Abstract

We define the Boolean center and the Boolean skeleton of a bounded BCK-algebra, and we use the Boolean skeleton to obtain a representation of bounded BCK-algebras, called (weak) Pierce \(b\mathbb{BCK}\)-representation, as (weak) Boolean products of bounded BCK-algebras. We analyze the cases in which the stalks in these representations are directly indecomposable, finitely subdirectly irreducible or simple algebras. We give some examples of algebras and relative subvarieties of bounded BCK-algebras to illustrate the results.

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Authors and Affiliations

  1. Facultat de Matemàtiques, Universitat de Barcelona, Gran Via 585, Pati de Ciencies 2a planta, 08007, Barcelona, Spain

    Joan Gispert & Antoni Torrens

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  1. Joan Gispert
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  2. Antoni Torrens
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Correspondence to Antoni Torrens.

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Gispert, J., Torrens, A. Boolean representation of bounded BCK-algebras. Soft Comput 12, 941–954 (2008). https://doi.org/10.1007/s00500-007-0261-0

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