×

On the lattice of ideals of an MV-algebra. (English) Zbl 1019.06004

The authors claim to have proved (Theorem 2.8) that the set of ideals of an MV-algebra \(A\) forms a Boolean lattice (under some natural operations) if and only if \(A\) is a finite Boolean lattice relative to its natural ordering. The proof depends on Proposition 2.3, which in turn depends on Lemma 1.5. However, there is an error in the proof of this Lemma, namely, a distributive law which does not exist is used. In fact, Lemma 1.5 is true if and only if the MV-algebra is a Boolean algebra.
Reviewer: C.S.Hoo (Edmonton)

MSC:

06D35 MV-algebras
03G25 Other algebras related to logic
PDFBibTeX XMLCite