Galois Connections and Applications by K Denecke

Galois Connections and Applications by K Denecke

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".

From the reviews:

"The book under review is the first one fully dedicated to Galois connections and adjunctions… I recommend this valuable collection to everybody involved in algebraic research and/or teaching algebra in higher education." (Béla Csákány, Acta Scientiarum Mathematicarum, Vol. 71, 2005)

SKU	Unavailable
ISBN 13	9789048165407
ISBN 10	9048165407
Title	Galois Connections and Applications
Author	K Denecke
Series	Mathematics And Its Applications
Condition	Unavailable
Binding Type	Paperback
Publisher	Springer
Year published	2010-12-07
Number of pages	502
Cover note	Book picture is for illustrative purposes only, actual binding, cover or edition may vary.