Boolean representation of bounded BCK-algebras |
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Authors: | Joan Gispert Antoni Torrens |
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Affiliation: | (1) Facultat de Matemàtiques, Universitat de Barcelona, Gran Via 585, Pati de Ciencies 2a planta, 08007 Barcelona, Spain |
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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 -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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Keywords: | Bounded BCK-algebras Boolean factor elements Weak Boolean product Pierce BCK-representation |
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