On pseudo-BL algebras and BCC-algebras

Authors:
Xiao-hong Zhang;Hua Li
Affiliations:
Faculty of Science, Ningbo University, 315211, Ningbo, Zhejiang Province, Peoples Republic of China;School of Computer Science, Northwestern Polytechnical University, 710072, Xi’an, Shaanxi Province, Peoples Republic of China
Venue:
Soft Computing - A Fusion of Foundations, Methodologies and Applications
Year:
2006

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Abstract

We further study the filter theory of pseudo-BL algebras. We give some equivalent conditions of filter, normal filter and Boolean filter. We introduce the notion of pseudo MV-filter, pseudo-G filter and characterize Boolean algebras, pseudo-MV algebras and pseudo Gödel algebras (i.e. Gödel algebras) in pseudo-BL algebras. We establish the connections between BCC-algebras, pseudo-BCK algebras, pseudo-BL algebras and weak pseudo-BL algebras (pseudo-MTL algebras).