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. (shrink)

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. (shrink)

The notion of monadic three-valued ukasiewicz algebras was introduced by L. Monteiro ([12], [14]) as a generalization of monadic Boolean algebras. A. Monteiro ([9], [10]) and later L. Monteiro and L. Gonzalez Coppola [17] obtained a method for the construction of a three-valued ukasiewicz algebra from a monadic Boolea algebra. In this note we give the construction of a monadic three-valued ukasiewicz algebra from a Boolean algebra B where we have defined two quantification operations and * such that *x=*x (where (...) *x=-*-x). In this case we shall say that and * commutes. If B is finite and is an existential quantifier over B, we shall show how to obtain all the existential quantifiers * which commute with .Taking into account R. Mayet [3] we also construct a monadic three-valued ukasiewicz algebra from a monadic Boolean algebra B and a monadic ideal I of B. (shrink)