Relevant bibliographies by topics / Lattice-ordered abelian groups

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters

Academic literature on the topic 'Lattice-ordered abelian groups'

Author: Grafiati
Published: 10 March 2023
Last updated: 31 July 2025

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Journal articles on the topic "Lattice-ordered abelian groups"

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Jakubík, Ján. "Retracts of abelian lattice ordered groups." Czechoslovak Mathematical Journal 39, no. 3 (1989): 477–85. http://dx.doi.org/10.21136/cmj.1989.102319.

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Glass, A. M. W. "Weakly abelian lattice-ordered groups." Proceedings of the American Mathematical Society 129, no. 3 (2000): 677–84. http://dx.doi.org/10.1090/s0002-9939-00-05706-3.

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Conrad, Paul, and J. Roger Teller. "Abelian pseudo lattice ordered groups." Publicationes Mathematicae Debrecen 17, no. 1-4 (2022): 223–41. http://dx.doi.org/10.5486/pmd.1970.17.1-4.26.

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Glass, A. M. W., Angus Macintyre, and Françoise Point. "Free abelian lattice-ordered groups." Annals of Pure and Applied Logic 134, no. 2-3 (2005): 265–83. http://dx.doi.org/10.1016/j.apal.2004.10.017.

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Di Nola, Antonio, Giacomo Lenzi, Gaetano Vitale, and Roberto Giuntini. "Expanding Lattice Ordered Abelian Groups to Riesz Spaces." Mathematica Slovaca 72, no. 1 (2022): 1–10. http://dx.doi.org/10.1515/ms-2022-0001.

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Abstract 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 improving a previous paper where the example was a non-totally ordered lattice ordered abelian group. This answers a question raised by Conrad in 1975. We give also a partial solution to another problem considered in the same paper. Finally, we apply our results to MV-algebras and Riesz MV-algebras.
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Glass, A. M. W. "Finitely presented ordered groups." Proceedings of the Edinburgh Mathematical Society 33, no. 2 (1990): 299–301. http://dx.doi.org/10.1017/s0013091500018204.

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Ploščica, Miroslav. "Cevian properties in ideal lattices of Abelian ℓ-groups". Forum Mathematicum 33, № 6 (2021): 1651–58. http://dx.doi.org/10.1515/forum-2021-0074.

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Abstract We consider the problem of describing the lattices of compact ℓ {\ell} -ideals of Abelian lattice-ordered groups. (Equivalently, describing the spectral spaces of Abelian lattice-ordered groups.) It is known that these lattices have countably based differences and admit a Cevian operation. Our first result says that these two properties are not sufficient: there are lattices having both countably based differences and Cevian operations, which are not representable by compact ℓ {\ell} -ideals of Abelian lattice-ordered groups. As our second result, we prove that every completely normal
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Gluschankof, Daniel, and François Lucas. "Hyper-regular lattice-ordered groups." Journal of Symbolic Logic 58, no. 4 (1993): 1342–58. http://dx.doi.org/10.2307/2275147.

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It is a well-known fact that the notion of an archimedean order cannot be formalized in the first-order calculus. In [12] and [18], A. Robinson and E. Zakon characterized the elementary class generated by all the archimedean, totally-ordered abelian groups (o-groups) in the language 〈+,<〉, calling it the class of regularly ordered or generalized archimedean abelian groups. Since difference (−) and 0 are definable in that language, it is immediate that in the expanded language 〈 +, −, 0, < 〉 the definable expansion of the class of regular groups is also the elementary class generated by t
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Glass, A. M. W. "Corrigendum to “Weakly Abelian lattice-ordered groups”." Proceedings of the American Mathematical Society 130, no. 3 (2001): 925–26. http://dx.doi.org/10.1090/s0002-9939-01-06502-9.

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Cignoli, R., D. Gluschankof, and F. Lucas. "Prime spectra of lattice-ordered abelian groups." Journal of Pure and Applied Algebra 136, no. 3 (1999): 217–29. http://dx.doi.org/10.1016/s0022-4049(98)00031-0.

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Dissertations / Theses on the topic "Lattice-ordered abelian groups"

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Russo, Anna Carla. "MV-algebras, Grothendieck toposes and applications." Doctoral thesis, Universita degli studi di Salerno, 2016. http://hdl.handle.net/10556/2308.

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2014 - 2015<br>This thesis is a contribution to the research program ‘toposes as bridges’ introduced in [12], which aims at developing the unifying potential of the notion of Grothendieck topos as a means for relating different mathematical theories to each other through topos-theoretic invariants. The general methodology outlined therein is applied here to study already existing categorical equivalences of particular interest arising in the field of many-valued logics and also to produce new ones. The original content of the disseration is contained in [22], [21] and [23]... [edited by A
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Books on the topic "Lattice-ordered abelian groups"

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Caramello, Olivia. Examples of theories of presheaf type. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198758914.003.0011.

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This chapter discusses several classical as well as new examples of theories of presheaf type from the perspective of the theory developed in the previous chapters. The known examples of theories of presheaf type that are revisited in the course of the chapter include the theory of intervals (classified by the topos of simplicial sets), the theory of linear orders, the theory of Diers fields, the theory of abstract circles (classified by the topos of cyclic sets) and the geometric theory of finite sets. The new examples include the theory of algebraic (or separable) extensions of a given field
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Book chapters on the topic "Lattice-ordered abelian groups"

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Weispfenning, Volker. "Model Theory of Abelian l-Groups." In Lattice-Ordered Groups. Springer Netherlands, 1989. http://dx.doi.org/10.1007/978-94-009-2283-9_4.

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Darnel, Michael R. "Representable and Abelian Ω-groups." In Theory of Lattice-Ordered Groups. CRC Press, 2021. http://dx.doi.org/10.1201/9781003067337-9.

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Mundici, Daniele. "Computing on Lattice-Ordered Abelian Groups." In Fields of Logic and Computation III. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-48006-6_15.

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Glass, A. M. W., and Françoise Point. "Finitely Presented Abelian Lattice-Ordered Groups." In Lecture Notes in Computer Science. Springer Berlin Heidelberg, 2007. http://dx.doi.org/10.1007/978-3-540-75939-3_11.

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"Abelian and Normal-valued Lattice-ordered Groups." In Series in Algebra. WORLD SCIENTIFIC, 1999. http://dx.doi.org/10.1142/9789812816184_0004.

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Journal articles
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