Abstract
In this paper, we study the class of all monadic implicational subreducts, that is, the \({\{\rightarrow, \forall,1\}}\)-subreducts of the class of monadic MV-algebras. We prove that this class is an equational class, which we denote by \({\mathcal{ML}}\), and we give an equational basis for this variety. An algebra in \({\mathcal{ML}}\) is called a monadic Łukasiewicz implication algebra. We characterize the subdirectly irreducible members of \({\mathcal{ML}}\) and the congruences of every monadic Łukasiewicz implication algebra by monadic filters. We prove that \({\mathcal{ML}}\) is generated by its finite members. Finally, we completely describe the lattice of subvarieties, and we give an equational basis for each proper subvariety.
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Presented by C. Tsinakis.
The support of CONICET is gratefully acknowledged.
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Cimadamore, C.R., Díaz Varela, J.P. Monadic MV-algebras II: Monadic implicational subreducts. Algebra Univers. 71, 201–219 (2014). https://doi.org/10.1007/s00012-014-0277-0
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DOI: https://doi.org/10.1007/s00012-014-0277-0