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January 24, 20260 citations

Some results on pseudo MV-algebras with n-roots

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CXChen XinrongHLHongxing Liu

Key Points

  • The aim is to explore the properties of pseudo MV-algebras with n-roots and their relationships to other algebraic structures.
  • Outlined the main properties of pseudo MV-algebras with n-roots
  • Introduced the concept of strict n-roots
  • Demonstrated equivalence with n-divisible unital l-groups
  • Explored relationships between strongly atomless pseudo MV-algebras and strict pseudo MV-algebras
  • Established that MV-algebras with n-roots form a variety
  • Classified pseudo MV-algebras with n-roots using strict n-roots
  • Found an equivalence between the variety and n-divisible unital l-groups
  • Identified a relationship between strongly atomless pseudo MV-algebras and strict pseudo MV-algebras

Abstract

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 -groups. Finally, we find a relationship between strongly atomless pseudo MV-algebra and strict pseudo MV-algebras. \\ Keywords: Pseudo MV-algebra; Square root; n-root; n-strict MV-algebra; Boolean algebra; Strongly atomless

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Cite This Study

Xinrong et al. (2025) studied this question.

synapsesocial.com/papers/697461a8bb9d90c67120b935https://doi.org/10.23755/rm.v55i0.1722
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