Strict MV-algebras
The aim of this paper is to go deeper into the questions of MV-algebras provided with square roots. Höhle proposed a classification of MV-algebras with square roots, introducing the strict MV-algebras and proving that every MV-algebra with square roots is exactly a Boolean algebra, or a strict algebra, or isomorphic to the product of both. Due to their important role we propose a characterization of strict MV-algebras proving that the following concepts are equivalent: (i) strict MV-algebras, (ii) 2-atomless MV-algebras. Moreover we show that a strict MV-algebra contains for every \(n \in N\), \(n\geq 0\), cyclic elements of order \(2^{n+1}\) and we find again the result of Höhle that their generated subalgebra is the set of rational dyadic numbers. Then, referring to the homomorphisms between MV-algebras, we prove that the homomorphic image of a strict MV-algebra is still a strict MV-algebra. \(\copyright\) Academic Press.
scientific article; zbMATH DE number 1348151