In this paper we define maximal MV-algebras, a concept similar to the maximal rings and maximal distributive lattices. We prove that any maximal MV-algebra is semilocal, then we characterize a maximal MV-algebra as finite direct product of local maximal MV-algebras.

Modal pseudocomplemented De Morgan algebras (or $mpM$-algebras for short) are investigated in this paper. This new equational class of algebras was introduced by A. V. Figallo and P. Landini ([Figallo, A. V., Landini, P.: Notes on $4$-valued modal algebras Preprints del Instituto de Ciencias Básicas, Univ. Nac. de San Juan 1 (1990), 28–37.]) and they constitute a proper subvariety of the variety of all pseudocomplemented De Morgan algebras satisfying $x\wedge {(\sim x)}^{*}={(\sim (x\wedge {(\sim x)}^{*}))}^{*}$. Firstly, a topological duality for these algebras...

We show that an ideal I of an MV-algebra A is linearly ordered if and only if every non-zero element of I is a molecule. The set of molecules of A is contained in Inf(A) ∪ B2(A) where B2(A) is the set of all elements x ∈ A such that 2x is idempotent. It is shown that I ≠ {0} is weakly essential if and only if B⊥ ⊂ B(A). Connections are shown among the classes of ideals that have various combinations of the properties of being implicative, essential, weakly essential, maximal or prime.

Here we initiate an investigation into the class $mL{M}_{n\times m}$ of monadic $n\times m$-valued Łukasiewicz-Moisil algebras (or $mL{M}_{n\times m}$-algebras), namely $n\times m$-valued Łukasiewicz-Moisil algebras endowed with a unary operation. These algebras constitute a generalization of monadic $n$-valued Łukasiewicz-Moisil algebras. In this article, the congruences on these algebras are determined and subdirectly irreducible algebras are characterized. From this last result it is proved that $mL{M}_{n\times m}$ is a discriminator variety and as a consequence, the...