Hyper‐Archimedean BL‐algebras are MV‐algebras | Zendy

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Hyper‐Archimedean BL‐algebras are MV‐algebras

Author(s) -

Turunen Esko

Publication year - 2007

Publication title -

mathematical logic quarterly

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.473

H-Index - 28

eISSN - 1521-3870

pISSN - 0942-5616

DOI - 10.1002/malq.200610037

Subject(s) - complete boolean algebra , stone's representation theorem for boolean algebras , free boolean algebra , boolean algebras canonically defined , boolean algebra , mathematics , two element boolean algebra , interior algebra , relation algebra , algebra over a field , discrete mathematics , pure mathematics , combinatorics , subalgebra , algebra representation , division algebra

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 , x n 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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