2 research outputs found
Maximal Subalgebras of MVn-algebras. A Proof of a Conjecture of A. Monteiro
For each integer n ≥ 2, MVn denotes the variety of MV-algebras generated by the MV-chain with n elements. Algebras in MVn 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 MVn are characterized, and it is shown that proper subalgebras are intersection of maximal subalgebras. When A ∈ MV3, 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.Fil: Cignoli, Roberto Leonardo Oscar. Consejo Nacional de Investigaciones CientÃficas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderon; ArgentinaFil: Monteiro, Luis. Consejo Nacional de Investigaciones CientÃficas y Técnicas. Centro CientÃfico Tecnológico Conicet - BahÃa Blanca. Instituto de Matemática BahÃa Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática BahÃa Blanca; Argentin