Galois Connections and Applications (Hardcover, 2004 ed.)

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.""

General

Imprint:	Springer-Verlag New York
Country of origin:	United States
Series:	Mathematics and Its Applications, 565
Release date:	March 2004
First published:	2004
Editors:	K. Denecke • M. Erne • S.L. Wismath
Dimensions:	235 x 155 x 28mm (L x W x T)
Format:	Hardcover
Pages:	502
Edition:	2004 ed.
ISBN-13:	978-1-4020-1897-8
Categories:	Books > Science & Mathematics > Mathematics > Algebra > General Promotions
LSN:	1-4020-1897-5
Barcode:	9781402018978

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