Some results on pseudo MV-algebras with n-roots

The paper provides a study of pseudo MV-algebras with $n$-roots. We outline their main properties and establish that the class of MV-algebras with $n$-roots forms a variety. Then, we introduce the concept of a strict $n$-root to classify the class of pseudo MV-algebras with $n$-root and demonstrate an equivalence between this variety and the class of $n$-divisible unital $\ell$-groups. Finally, we find a relationship between strongly atomless pseudo MV-algebra and strict pseudo MV-algebras. \\ \textbf{Keywords}: Pseudo MV-algebra; Square root; n-root; n-strict MV-algebra; Boolean algebra; Strongly atomless