Combining Boolean algebras and \(\ell \)-groups in the variety generated by Chang's MV-algebra (Q2822857)

Every MV-algebra \(A\) has two important parts: the Boolean skeleton formed by all Boolean elements, and the perfect skeleton formed by all infinitesimal and co-infinitesimal elements of \(A\).NEWLINENEWLINEThe paper under review studies a construction of an MV-algebra \(A\) from a Boolean algebra \(B\) and a perfect MV-algebra \(P\) such that its Boolean skeleton is isomorphic to \(B\) and its perfect skeleton is isomorphic to \(P\). In the paper, such a construction is presented, and it is noted that this is not the unique way. In addition, the question is studied whether every MV-algebra in the variety generated by the Chang MV-algebra has a perfect skeleton as a quotient. It is shown that the answer is negative and the class of such MV-algebras is axiomatized.