| 書目名稱 | The Theory of Lattice-Ordered Groups | | 編輯 | V. M. Kopytov,N. Ya. Medvedev | | 視頻video | http://file.papertrans.cn/922/921141/921141.mp4 | | 叢書名稱 | Mathematics and Its Applications | | 圖書封面 |  | | 描述 | 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 mathemat- ics bound up with its fundamentals. For example, the classification of infinitesimals resulted in discovery of non-archimedean ordered al- gebraic systems, the formalization of the notion of real number led to the definition of ordered groups and ordered fields, the construc- tion 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 exam- ple, partially ordered groups with interpolation property were intro- duced in F. Riesz‘s fundamental paper [1] as a key to his investigations of partially ordered real vec | | 出版日期 | Book 1994 | | 關(guān)鍵詞 | Group theory; Lattice; algebra; semigroup | | 版次 | 1 | | doi | https://doi.org/10.1007/978-94-015-8304-6 | | isbn_softcover | 978-90-481-4474-7 | | isbn_ebook | 978-94-015-8304-6 | | copyright | Springer Science+Business Media Dordrecht 1994 |
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