Maximal subalgebras of MV_n-algebras. A proof of a conjecture of A.

CIGNOLI, ROBERTO LEONARDO OSCAR; MONTEIRO, LUIZ

STUDIA LOGICA

Springer Verlag

Año: 2006 vol. 84 p. 393 - 495

0039-3215

For each integer n ¡Ý2, MV_n denotes the variety of MV-algebras generated by the MV-chain with n elements. Algebras in MV_n are represented as continuous functions from a Boolean space into a n-element chain equipped with the discrete topology. Using these representations, maximal subalgebras of algebras in MV_n are characterized, and it is shown that proper subalgebras are intersection of maximal subalgebras. When A is in MV_3,  the mentioned characterization of maximal subalgebras of A can be given in terms of prime filters of the underlying lattice of A, in the form that was conjectured by A. Monteiro.