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On half lattice ordered groups [PDF]
, 1996 summary:The notion of the half linearly ordered group (and, more generally, of the half lattice ordered group) was introduced by Giraudet and Lucas [2]. In the present paper we define the lexicographic product of half linearly ordered groups.
Jakubík, Ján +2 more
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$\alpha$-Projectable and laterally $\alpha$-complete Archimedean lattice-ordered groups with weak unit via topology [PDF]
Categories and General Algebraic Structures with ApplicationsLet $\bf{W}$ be the category of Archimedean lattice-ordered groups with weak order unit, $\bf{Comp}$ the category of compact Hausdorff spaces, and $\mathbf{W} \xrightarrow{Y} \mathbf{Comp}$ the Yosida functor, which represents a $\bf{W}$-object $A$ as ...
Brian Wynne, Anthony Hager
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Cardinality of the system of all sequential convergences on an Abelian lattice ordered group [PDF]
, 1987 Sequential convergences on groups were investigated by J. Novák in [11], cf. also the surveys of R. Frič and V. Koutnik [4, 5]. The notion of sequential convergence on an abelian lattice ordered group was introduced in [8] ; the non-abelian case was ...
Jakubík, Ján +3 more
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Large off-diagonal magnetoelectricity in a triangular Co2+-based collinear antiferromagnet
Nature Communications, 2023 Magnetic toroidicity is an uncommon type of magnetic structure in solid-state materials. Here, we experimentally demonstrate that collinear spins in a material with R-3 lattice symmetry can host a significant magnetic toroidicity, even parallel to the ...
Xianghan Xu +8 more
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On lattice-ordered monoids [PDF]
, 2003 In the paper lattice-ordered monoids and specially normal lattice-ordered monoids which are a generalization of dually residuated lattice-ordered semigroups are investigated.
Jasem, Milan
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Valuations of Lattice-Ordered Groups
Journal of Algebra, 1997 The authors study valuations on lattice-ordered groups with values in a lattice of order ideals of the root system of regular subgroups. They use these valuations to obtain new and old results for archimedean extensions and archimedean closures of lattice-ordered groups. In the penultimate section of their paper, they define \(\Delta\)-extensions and \(
Conrad, Paul F. +2 more
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The Lebesgue state of a unital Abelian lattice-ordered group, II [PDF]
, 2009 We characterize the Lebesgue state of a free finitely generated unital lattice-ordered abelian group G in terms of its value at each element of each basis of G.
V. Marra
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Expanding lattice ordered abelian groups to Riesz spaces [PDF]
, 2022 First we give a necessary and sufficient condition for an abelian lattice ordered group to admit an expansion to a Riesz space (or vector lattice). Then we construct a totally ordered abelian group with two non-isomorphic Riesz space structures, thus ...
Di Nola, A., Vitale, G., Lenzi, G.
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A topology on lattice ordered groups [PDF]
Proceedings of the American Mathematical Society, 1998 We show that a lattice ordered group can be topologized in a natural way. The topology depends on the choice of a set C C ...
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The free lattice-ordered group over a nilpotent group [PDF]
, 1991 We show that the free lattice-ordered group over a finitely generated torsionfree nilpotent group is l l -solvable of some finite rank.
Michael R. Darnel
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