2022/10/17 by Dvurečenskij, Anatolij, Zahiri, Omid
#Commutative Algebra (math.AC) #FOS: Mathematics
paper · doi:10.48550/arxiv.2210.09350
The paper provides a study of pseudo MV-algebras with square roots. We introduce different notions of a square root on a pseudo MV-algebra, and present their main properties. We show that the class of pseudo-MV-algebras with square roots is a proper subvariety of the variety of pseudo MV-algebras. Then, we define a strict square root to classify the class of pseudo MV-algebras with square roots. We found a relationship between strongly atomless pseudo MV-algebras and strict pseudo MV-algebras. Finally, we investigate square roots on representable symmetric pseudo MV-algebras, and we present a complete characterization of a square root and a weak square root on a representable symmetric pseudo MV-algebra using addition in a unital ℓ-group. Some interesting examples are provided.