On EMV-algebras with square roots

2022/10/03 by Dvurečenskij, Anatolij, Zahiri, Omid
#Commutative Algebra (math.AC) #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2210.00862

Abstract

A square root is a unary operation with some special properties. In the paper, we introduce and study square roots on EMV-algebras. First, the known properties of square roots defined on MV-algebras will be generalized for EMV-algebras, and we also find some new ones for MV-algebras. We use square roots to characterize EMV-algebras. Then, we find a relation between the square root of an EMV-algebra and the square root on its representing EMV-algebra with top element. We show that each strict EMV-algebra has a top element and we investigate the relation between divisible EMV-algebras and EMV-algebras with a special square root. Finally, we present square roots on tribes, EMV-tribes, and we present a complete characterization of any square root on an MV-algebra and on an EMV-algebra by group addition in the corresponding unital ℓ-group.

Related

• Some results on pseudo MV-algebras with square roots
• Representation and Embedding of Pseudo MV-algebras with Square Roots I. Strict Square Roots
• Representation and Embedding of Pseudo MV-algebras with Square Roots II. Closures
• On EMV-algebras
• Morphisms on EMV-algebras and Their Applications