Perfect MV-algebras are categorically equivalent to abelianl-groups

Commutative rings whose ideals form an MV‐algebra

“…Generally the relation of MV-algebras and rings follows the path of starting with a ring for which there is a naturally associated lattice ordered Abelian group, one then passes to an MV-algebra via the Mundici functor [15] or the Di Nola-Lettieri functor [9].…”

How Do $$\ell $$-Groups and Po-Groups Appear in Algebraic and Quantum Structures?

“…The class of perfect MValgebras is not a variety, but is a category. Di Nola and Lettieri (1994) characterized perfect MV-algebras as follows: The variety generated by perfect MV-algebras is also generated by Γ (Z − → × Z, (1, 0)) and is axiomatized relative to M V by the equation 2 x 2 = (2 x) 2 .…”

Discrete (n + 1)-valued states and n-perfect pseudo-effect algebras

“…In a perfect MV-algebra, every element belongs either to its radical or its coradical. In [7], it is shown that for any perfect MV-algebra M , there exists an Abelian unital ℓ-group G (lattice-ordered group), such that M is isomorphic to an interval of the lexicographic product of the group of integers Z and G.…”