Hyper-Archimedean BL-algebras are MV-algebras

Mathematical Logic Quarterly 53 (2):170-175 (2007)
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Abstract

Generalizations of Boolean elements of a BL-algebra L are studied. By utilizing the MV-center MV(L) of L, it is reproved that an element x L is Boolean iff x x * = 1. L is called semi-Boolean if for all x L, x * is Boolean. An MV-algebra L is semi-Boolean iff L is a Boolean algebra. A BL-algebra L is semi-Boolean iff L is an SBL-algebra. A BL-algebra L is called hyper-Archimedean if for all x L, xn is Boolean for some finite n 1. It is proved that hyper-Archimedean BL-algebras are MV-algebras. The study has application in mathematical fuzzy logics whose Lindenbaum algebras are MV-algebras or BL-algebras. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

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Citations of this work

BL-rings.O. A. Heubo-Kwegna, C. Lele, S. Ndjeya & J. B. Nganou - 2018 - Logic Journal of the IGPL 26 (3):290-299.

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Boolean deductive systems of BL-algebras.Esko Turunen - 2001 - Archive for Mathematical Logic 40 (6):467-473.

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