n-roots on MV-algebras

We 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 demonstrat...

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Bibliographic Details
Published inFuzzy sets and systems Vol. 484; p. 108930
Main Authors Dvurečenskij, A., Zahiri, O., Shenavaei, M., Borzooei, R.A.
Format Journal Article
LanguageEnglish
Published Elsevier B.V 15.05.2024
Subjects
Boolean algebra
MV-algebra
n-root
n-strict MV-algebra
Square root
Strongly atomless
Boolean algebra
Square root
Strongly atomless
n-root
n-strict MV-algebra
MV-algebra
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Summary:We 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 ℓ-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.
ISSN:0165-0114
1872-6801
DOI:10.1016/j.fss.2024.108930