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Mathematics > Rings and Algebras

arXiv:2210.00862 (math)
[Submitted on 3 Oct 2022]

Title:On EMV-algebras with square roots

Authors:Anatolij Dvurečenskij, Omid Zahiri
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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 $\ell$-group.
Subjects: Rings and Algebras (math.RA); Commutative Algebra (math.AC)
Cite as: arXiv:2210.00862 [math.RA]
  (or arXiv:2210.00862v1 [math.RA] for this version)
  https://doi.org/10.48550/arXiv.2210.00862

Submission history

From: Anatolij Dvurečenskij [view email]
[v1] Mon, 3 Oct 2022 12:27:38 UTC (29 KB)
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