Some results on pseudo MV-algebras with square roots

The paper provides a study of pseudo MV-algebras with square roots. We introduce different notions root on MV-algebra, and present their main properties. show that the class pseudo-MV-algebras roots is proper subvariety variety MV-algebras. Then, we define strict to classify found relationship between strongly atomless Finally, investigate representable symmetric MV-algebras, complete characterization weak MV-algebra using addition in unital ℓ-group. Some interesting examples are provided.