Browsing by Author "Verbovskiy V"

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    On Commutativity of Weakly o-Minimal Lattice Ordered Groups
    (Suleyman Demirel University, 2012) Verbovskiy V; Tulepbergenova I.
    A lattice-ordered structure is called weakly o-minimal if every definable subset can be represented as a finite union of convex sets. This paper investigates the properties of weakly o-minimal lattice-ordered groups, extending the notion of weak o-minimality from totally ordered groups to partially ordered lattice groups. We prove that such groups are Abelian, meaning all elements commute, divisible, so every element can be divided by any positive integer, and dense, implying no minimal positive elements exist. These results provide a deeper understanding of the algebraic and order-theoretic properties of partially ordered groups under weak o-minimality, highlighting their structural regularity and foundational behavior.