MV-algebras and their corresponding Bézout domains

The paper studies the interplay between MV-algebras, Bézout domains, and Abelian l-groups, which was initiated by Y. C. Yang in 2006. For each MV-algebra M=Γ(G,u), we delve into some properties of a subset of a Bézout domain corresponding to M. We study Boolean elements and ideals within the MV-algebra, focusing on their correspondence to subsets of Bézout domains. This investigation aids us in classifying Bézout domains about directly indecomposable MV-algebras or subdirect products of MV-algebras. We establish that each MV-algebra associated with a Noetherian Bézout domain is finite. In conclusion, from a ring-theoretical perspective, we present characteristics of perfect MV-algebras, (H,1)-perfect MV-algebras, hyperarchimedean MV-algebras, and complete MV-algebras.