Representation and Embedding of Pseudo MV-algebras with Square Roots I. Strict Square Roots

In [17], we started the investigation of pseudo MV-algebras with square roots. In the present paper, we continue to study the structure of pseudo MV- algebras with square roots focusing on their new characterizations. The paper is divided into two parts. In the present first part, we investigate the relationship between a pseudo MV-algebra with square root and its corresponding unital ℓ-group in the scene of two-divisibility. We characterize strict and non-strict square roots and we describe square roots on strongly (H, 1)-perfect pseudo MV-algebras. In the second part, we find some conditions under which a particular class of pseudo MV-algebras can be embedded into pseudo MV-algebras with square ∗ The paper acknowledges the support by the grant of the Slovak Research and Development Agency under contract APVV-20-0069 and the grant VEGA No. 2/0142/20 SAV, A. D † The project was also funded by the European Union’s Horizon 2020 Research and Innovation Programme on the basis of the Grant Agreement under the Marie Skłodowska-Curie funding scheme No. 945478 - SASPRO 2, project 1048/01/01, O. Z ‡ Corresponding Author: Omid Zahiri

Authors

• Anatolij Dvurečenskij
• Omid Zahiri

Keywords

• Pseudo MV-algebra
• unital ℓ-group
• symmetric pseudo MV-algebra
• square root
• strict square root
• square root closure
• two-divisibility
• divisibility
• embedding