The Theory of Lattice-Ordered Groups:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht
Springer Netherlands
1994
|
| Schriftenreihe: | Mathematics and Its Applications
307 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | A partially ordered group is an algebraic object having the structure of a group and the structure of a partially ordered set which are connected in some natural way. These connections were established in the period between the end of 19th and beginning of 20th century. It was realized that ordered algebraic systems occur in various branches of mathematics bound up with its fundamentals. For example, the classification of infinitesimals resulted in discovery of non-archimedean ordered algebraic systems, the formalization of the notion of real number led to the definition of ordered groups and ordered fields, the construction of non-archimedean geometries brought about the investigation of non-archimedean ordered groups and fields. The theory of partially ordered groups was developed by: R. Dedekind, a. Holder, D. Gilbert, B. Neumann, A. I. Mal'cev, P. Hall, G. Birkhoff. These connections between partial order and group operations allow us to investigate the properties of partially ordered groups. For example, partially ordered groups with interpolation property were introduced in F. Riesz's fundamental paper [1] as a key to his investigations of partially ordered real vector spaces, and the study of ordered vector spaces with interpolation properties were continued by many functional analysts since. The deepest and most developed part of the theory of partially ordered groups is the theory of lattice-ordered groups. In the 40s, following the publications of the works by G. Birkhoff, H. Nakano and P. |
| Beschreibung: | 1 Online-Ressource (XVI, 400 p) |
| ISBN: | 9789401583046 9789048144747 |
| DOI: | 10.1007/978-94-015-8304-6 |
Internformat
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| 490 | 1 | |a Mathematics and Its Applications |v 307 | |
| 500 | |a A partially ordered group is an algebraic object having the structure of a group and the structure of a partially ordered set which are connected in some natural way. These connections were established in the period between the end of 19th and beginning of 20th century. It was realized that ordered algebraic systems occur in various branches of mathematics bound up with its fundamentals. For example, the classification of infinitesimals resulted in discovery of non-archimedean ordered algebraic systems, the formalization of the notion of real number led to the definition of ordered groups and ordered fields, the construction of non-archimedean geometries brought about the investigation of non-archimedean ordered groups and fields. The theory of partially ordered groups was developed by: R. Dedekind, a. Holder, D. Gilbert, B. Neumann, A. I. Mal'cev, P. Hall, G. Birkhoff. These connections between partial order and group operations allow us to investigate the properties of partially ordered groups. For example, partially ordered groups with interpolation property were introduced in F. Riesz's fundamental paper [1] as a key to his investigations of partially ordered real vector spaces, and the study of ordered vector spaces with interpolation properties were continued by many functional analysts since. The deepest and most developed part of the theory of partially ordered groups is the theory of lattice-ordered groups. In the 40s, following the publications of the works by G. Birkhoff, H. Nakano and P. | ||
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Datensatz im Suchindex
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| author | Kopytov, V. M. |
| author_facet | Kopytov, V. M. |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
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| discipline | Mathematik |
| doi_str_mv | 10.1007/978-94-015-8304-6 |
| format | Electronic eBook |
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| institution | BVB |
| isbn | 9789401583046 9789048144747 |
| language | English |
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| spelling | Kopytov, V. M. Verfasser aut The Theory of Lattice-Ordered Groups by V. M. Kopytov, N. Ya. Medvedev Dordrecht Springer Netherlands 1994 1 Online-Ressource (XVI, 400 p) txt rdacontent c rdamedia cr rdacarrier Mathematics and Its Applications 307 A partially ordered group is an algebraic object having the structure of a group and the structure of a partially ordered set which are connected in some natural way. These connections were established in the period between the end of 19th and beginning of 20th century. It was realized that ordered algebraic systems occur in various branches of mathematics bound up with its fundamentals. For example, the classification of infinitesimals resulted in discovery of non-archimedean ordered algebraic systems, the formalization of the notion of real number led to the definition of ordered groups and ordered fields, the construction of non-archimedean geometries brought about the investigation of non-archimedean ordered groups and fields. The theory of partially ordered groups was developed by: R. Dedekind, a. Holder, D. Gilbert, B. Neumann, A. I. Mal'cev, P. Hall, G. Birkhoff. These connections between partial order and group operations allow us to investigate the properties of partially ordered groups. For example, partially ordered groups with interpolation property were introduced in F. Riesz's fundamental paper [1] as a key to his investigations of partially ordered real vector spaces, and the study of ordered vector spaces with interpolation properties were continued by many functional analysts since. The deepest and most developed part of the theory of partially ordered groups is the theory of lattice-ordered groups. In the 40s, following the publications of the works by G. Birkhoff, H. Nakano and P. Mathematics Group theory Algebra Logic, Symbolic and mathematical Order, Lattices, Ordered Algebraic Structures Group Theory and Generalizations Mathematical Logic and Foundations Mathematik Verbandsgruppe (DE-588)4285609-7 gnd rswk-swf Verbandsgruppe (DE-588)4285609-7 s 1\p DE-604 Medvedev, N. Ya Sonstige oth Mathematics and Its Applications 307 (DE-604)BV008163334 307 https://doi.org/10.1007/978-94-015-8304-6 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Kopytov, V. M. The Theory of Lattice-Ordered Groups Mathematics and Its Applications Mathematics Group theory Algebra Logic, Symbolic and mathematical Order, Lattices, Ordered Algebraic Structures Group Theory and Generalizations Mathematical Logic and Foundations Mathematik Verbandsgruppe (DE-588)4285609-7 gnd |
| subject_GND | (DE-588)4285609-7 |
| title | The Theory of Lattice-Ordered Groups |
| title_auth | The Theory of Lattice-Ordered Groups |
| title_exact_search | The Theory of Lattice-Ordered Groups |
| title_full | The Theory of Lattice-Ordered Groups by V. M. Kopytov, N. Ya. Medvedev |
| title_fullStr | The Theory of Lattice-Ordered Groups by V. M. Kopytov, N. Ya. Medvedev |
| title_full_unstemmed | The Theory of Lattice-Ordered Groups by V. M. Kopytov, N. Ya. Medvedev |
| title_short | The Theory of Lattice-Ordered Groups |
| title_sort | the theory of lattice ordered groups |
| topic | Mathematics Group theory Algebra Logic, Symbolic and mathematical Order, Lattices, Ordered Algebraic Structures Group Theory and Generalizations Mathematical Logic and Foundations Mathematik Verbandsgruppe (DE-588)4285609-7 gnd |
| topic_facet | Mathematics Group theory Algebra Logic, Symbolic and mathematical Order, Lattices, Ordered Algebraic Structures Group Theory and Generalizations Mathematical Logic and Foundations Mathematik Verbandsgruppe |
| url | https://doi.org/10.1007/978-94-015-8304-6 |
| volume_link | (DE-604)BV008163334 |
| work_keys_str_mv | AT kopytovvm thetheoryoflatticeorderedgroups AT medvedevnya thetheoryoflatticeorderedgroups |