Galois Connections and Applications is popular PDF and ePub book, written by K. Denecke in 2013-11-11, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, Galois Connections and Applications can be Read Online from any device for your convenience.
Galois Connections and Applications Book PDF Summary
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" objects (the fixed points of the composite maps) leads to a precise "duality between two maximal subworlds".
Detail Book of Galois Connections and Applications PDF
- Author : K. Denecke
- Release : 11 November 2013
- Publisher : Springer Science & Business Media
- ISBN : 9781402018985
- Genre : Mathematics
- Total Page : 511 pages
- Language : English
- PDF File Size : 11,5 Mb
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