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Galois theories

Borceux, Francis, (1948-)

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Galois theories

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Galois theories/ Francis Borceux, George Janelidze.
作者:	Borceux, Francis,
其他作者:	Janelidze, G.
出版者:	Cambridge :Cambridge University Press, : 2001.,
面頁冊數:	xiv, 341 p. :ill., digital ;24 cm.
附註:	Title from publisher's bibliographic system (viewed on 05 Oct 2015).
標題:	Galois theory. -
電子資源:	https://doi.org/10.1017/CBO9780511619939
ISBN:	9780511619939

Galois theories
Borceux, Francis,1948-

Galois theories[electronic resource] /Francis Borceux, George Janelidze. - Cambridge :Cambridge University Press,2001. - xiv, 341 p. :ill., digital ;24 cm. - Cambridge studies in advanced mathematics ;72. - Cambridge studies in advanced mathematics ;72..

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Classical galois theory --

Starting from the classical finite-dimensional Galois theory of fields, this book develops Galois theory in a much more general context, presenting work by Grothendieck in terms of separable algebras and then proceeding to the infinite-dimensional case, which requires considering topological Galois groups. In the core of the book, the authors first formalize the categorical context in which a general Galois theorem holds, and then give applications to Galois theory for commutative rings, central extensions of groups, the topological theory of covering maps and a Galois theorem for toposes. The book is designed to be accessible to a wide audience: the prerequisites are first courses in algebra and general topology, together with some familiarity with the categorical notions of limit and adjoint functors. The first chapters are accessible to advanced undergraduates, with later ones at a graduate level. For all algebraists and category theorists this book will be a rewarding read.

ISBN: 9780511619939Subjects--Topical Terms:

523821
Galois theory.

LC Class. No.: QA214 / .B67 2001

Dewey Class. No.: 512.3

Galois theories
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500 $a Title from publisher's bibliographic system (viewed on 05 Oct 2015).
505 0 0 $t Classical galois theory -- $t Galois theory of grothendieck -- $t Infinitary galois theory -- $t Categorical galois theory of commuttive rings -- $t Categorical galois theorem and factorization systems -- $t Covering maps -- $t Non-galoisian galois theory.
520 $a Starting from the classical finite-dimensional Galois theory of fields, this book develops Galois theory in a much more general context, presenting work by Grothendieck in terms of separable algebras and then proceeding to the infinite-dimensional case, which requires considering topological Galois groups. In the core of the book, the authors first formalize the categorical context in which a general Galois theorem holds, and then give applications to Galois theory for commutative rings, central extensions of groups, the topological theory of covering maps and a Galois theorem for toposes. The book is designed to be accessible to a wide audience: the prerequisites are first courses in algebra and general topology, together with some familiarity with the categorical notions of limit and adjoint functors. The first chapters are accessible to advanced undergraduates, with later ones at a graduate level. For all algebraists and category theorists this book will be a rewarding read.
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