Dvure?enskij, A.Zahiri, O.Shenavaei, M.Borzooei, R.A.2024-05-192024-05-1920240165-0114https://doi.org/10.1016/j.fss.2024.108930https://hdl.handle.net/20.500.12713/4257We introduce and investigate n-roots in the context of MV-algebras as a generalization of square roots introduced in [16]. We outline their main properties and establish that the class of MV-algebras with n-roots, MVnr, forms a variety. Next, we introduce the concept of strict n-roots and demonstrate an equivalence between MVnr and the class of n-divisible unital ?-groups. It helped us to show that each MV-algebra with an n-root is a direct product of an n-strict MV-algebra and a Boolean algebra. Finally, we delve into the connection between strongly atomless MV-algebras and MV-algebras with strict n-roots, demonstrating that in the context of MVnr, these concepts are equivalent. © 2024eninfo:eu-repo/semantics/closedAccessBoolean AlgebraMv-AlgebraN-RootN-Strict Mv-AlgebraSquare RootStrongly AtomlessArticle4842-s2.0-8518805234010.1016/j.fss.2024.108930Q1