| 书目名称 | Galois Connections and Applications | | 编辑 | K. Denecke,M. Erné,S. L. Wismath | | 视频video | | | 概述 | The only book to describe the use of Galois connections in a wide field of branches of mathematics and outside of mathematics | | 丛书名称 | Mathematics and Its Applications | | 图书封面 |  | | 描述 | Galois connections provide the order- or structure-preserving passage between two worlds of our imagination - and thus are inherent in hu man thinking wherever logical or mathematical reasoning about cer tain hierarchical structures is involved. Order-theoretically, a Galois connection is given simply by two opposite order-inverting (or order preserving) maps whose composition yields two closure operations (or one closure and one kernel operation in the order-preserving case). Thus, the "hierarchies" in the two opposite worlds are reversed or transported when passing to the other world, and going forth and back becomes a stationary process when iterated. The advantage of such an "adjoint situation" is that information about objects and relationships in one of the two worlds may be used to gain new information about the other world, and vice versa. In classical Galois theory, for instance, properties of permutation groups are used to study field extensions. Or, in algebraic geometry, a good knowledge of polynomial rings gives insight into the structure of curves, surfaces and other algebraic vari eties, and conversely. Moreover, restriction to the "Galois-closed" or "Galois-open | | 出版日期 | Book 2004 | | 关键词 | Algebra; Arithmetic; Category theory; Morphism; Topology; calculus; complexity; linguistics; mathematics; dat | | 版次 | 1 | | doi | https://doi.org/10.1007/978-1-4020-1898-5 | | isbn_softcover | 978-90-481-6540-7 | | isbn_ebook | 978-1-4020-1898-5 | | copyright | Springer Science+Business Media Dordrecht 2004 |
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发表于 2025-3-21 17:43:33
