Lattice-Ordered Groups: An Introduction
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht
Springer Netherlands
1988
|
| Schriftenreihe: | Reidel Texts in the Mathematical Sciences, A Graduate-Level Book Series
4 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | The study of groups equipped with a compatible lattice order ("lattice-ordered groups" or "I!-groups") has arisen in a number of different contexts. Examples of this include the study of ideals and divisibility, dating back to the work of Dedekind and continued by Krull; the pioneering work of Hahn on totally ordered abelian groups; and the work of Kantorovich and other analysts on partially ordered function spaces. After the Second World War, the theory of lattice-ordered groups became a subject of study in its own right, following the publication of fundamental papers by Birkhoff, Nakano and Lorenzen. The theory blossomed under the leadership of Paul Conrad, whose important papers in the 1960s provided the tools for describing the structure for many classes of I!-groups in terms of their convex I!-subgroups. A particularly significant success of this approach was the generalization of Hahn's embedding theorem to the case of abelian lattice-ordered groups, work done with his students John Harvey and Charles Holland. The results of this period are summarized in Conrad's "blue notes" [C] |
| Beschreibung: | 1 Online-Ressource (204p) |
| ISBN: | 9789400928718 9789401077927 |
| ISSN: | 0921-9315 |
| DOI: | 10.1007/978-94-009-2871-8 |
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| dewey-ones | 004 - Computer science |
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| dewey-tens | 000 - Computer science, information, general works |
| discipline | Physik Informatik |
| doi_str_mv | 10.1007/978-94-009-2871-8 |
| format | Electronic eBook |
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| spelling | Anderson, Marlow Verfasser aut Lattice-Ordered Groups An Introduction by Marlow Anderson, Todd Feil Dordrecht Springer Netherlands 1988 1 Online-Ressource (204p) txt rdacontent c rdamedia cr rdacarrier Reidel Texts in the Mathematical Sciences, A Graduate-Level Book Series 4 0921-9315 The study of groups equipped with a compatible lattice order ("lattice-ordered groups" or "I!-groups") has arisen in a number of different contexts. Examples of this include the study of ideals and divisibility, dating back to the work of Dedekind and continued by Krull; the pioneering work of Hahn on totally ordered abelian groups; and the work of Kantorovich and other analysts on partially ordered function spaces. After the Second World War, the theory of lattice-ordered groups became a subject of study in its own right, following the publication of fundamental papers by Birkhoff, Nakano and Lorenzen. The theory blossomed under the leadership of Paul Conrad, whose important papers in the 1960s provided the tools for describing the structure for many classes of I!-groups in terms of their convex I!-subgroups. A particularly significant success of this approach was the generalization of Hahn's embedding theorem to the case of abelian lattice-ordered groups, work done with his students John Harvey and Charles Holland. The results of this period are summarized in Conrad's "blue notes" [C] Computer science Computational complexity Computer Science Discrete Mathematics in Computer Science Informatik Verbandsgruppe (DE-588)4285609-7 gnd rswk-swf Verbandsgruppe (DE-588)4285609-7 s 1\p DE-604 Feil, Todd Sonstige oth https://doi.org/10.1007/978-94-009-2871-8 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Anderson, Marlow Lattice-Ordered Groups An Introduction Computer science Computational complexity Computer Science Discrete Mathematics in Computer Science Informatik Verbandsgruppe (DE-588)4285609-7 gnd |
| subject_GND | (DE-588)4285609-7 |
| title | Lattice-Ordered Groups An Introduction |
| title_auth | Lattice-Ordered Groups An Introduction |
| title_exact_search | Lattice-Ordered Groups An Introduction |
| title_full | Lattice-Ordered Groups An Introduction by Marlow Anderson, Todd Feil |
| title_fullStr | Lattice-Ordered Groups An Introduction by Marlow Anderson, Todd Feil |
| title_full_unstemmed | Lattice-Ordered Groups An Introduction by Marlow Anderson, Todd Feil |
| title_short | Lattice-Ordered Groups |
| title_sort | lattice ordered groups an introduction |
| title_sub | An Introduction |
| topic | Computer science Computational complexity Computer Science Discrete Mathematics in Computer Science Informatik Verbandsgruppe (DE-588)4285609-7 gnd |
| topic_facet | Computer science Computational complexity Computer Science Discrete Mathematics in Computer Science Informatik Verbandsgruppe |
| url | https://doi.org/10.1007/978-94-009-2871-8 |
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