2023/06/01 by Anatolij Dvurečenskij, Dvurečenskij, Anatolij, Omid Zahiri +1
Computer Science · #Advanced Algebra and Logic #Commutative Algebra (math.AC) #FOS: Mathematics #Rings and Algebras (math.RA) #Rough Sets and Fuzzy Logic
paper · pdf · doi:10.48550/arxiv.2306.04623
openalex publication_date 2023/06/01 · openalex created_date 2023/06/09 · openalex updated_date 2026/08/01
In \citeDvZa3, 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. 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 roots. We introduce and investigate the concepts of a strict square root of a pseudo MV-algebra and a square root closure, and we compare both notions. We show that each MV-algebra has a square root closure. Finally, using the square root of individual elements of a pseudo MV-algebra, we find the greatest subalgebra of a special pseudo MV-algebra with weak square root.