Research Catalog

Title

Taming wild extensions : Hopf algebras and local Galois module theory / Lindsay N. Childs.

Author

Childs, Lindsay.

Publication

Providence, R.I. : American Mathematical Society, ©2000.

Items in the Library & Off-site

Details

Description

viii, 215 pages; 27 cm.

Series Statement

Mathematical surveys and monographs, 0076-5376 ; v. 80

Uniform Title

Mathematical surveys and monographs ; no. 80.

Subject

• Hopf algebras
• Galois modules (Algebra)
• Field extensions (Mathematics)
• Álgebras de hopf
• Hopf, Algèbres de
• Modules galoisiens
• Extensions de corps (mathématiques)

Bibliography (note)

• Includes bibliographical references (p. 205-211) and index.

Additional Formats (note)

• Also available in an electronic version.

Contents

Hopf algebras and Galois extensions -- Basic definitions and notation -- Hopf algebras and R-algebras -- Integrals -- Short exact sequences of Hopf algebras -- Hopf orders -- Hopf Galois structures on separable field extensions -- Greither-Pareigis theory -- Byott's translation -- Byott's uniqueness theorem -- Prime power cyclic Galois extensions -- Non-abelian extensions -- Pure extensions -- Tame extensions and Noether's Theorem -- Associated orders -- Tame extensions -- Galois extensions -- Hopf algebras of rank p -- Rank p Hopf orders over algebraically closed fields -- Eigenspace decompositions -- Larson orders -- Group valuations -- Orders from valuations -- Lattice properties -- Uniqueness results -- One-parameter Larson orders -- Cyclic extensions of degree p -- Different and discriminant -- Ramification groups -- Cyclic extensions of degree p -- Non-maximal orders -- Hopf Galois orders in Kummer extensions of order p -- Orders and associated orders -- Ramification restrictions -- Ramification numbers -- Tameness -- When does tame imply Galois -- Ramification conditions -- Hopf algebras of rank p[superscript 2] -- Hopf orders in KC[subscript p superscript 2] -- Cyclic Hopf Galois extensions of degree p[superscript 2] -- Valuation rings of cyclic extensions of degree p[superscript 2] -- Formal groups -- Formal groups -- Formal groups and Hopf algebras -- Height -- Lubin-Tate formal groups -- Oort embedding -- Polynomial formal groups -- Principal homogeneous spaces and formal groups -- Kummer extensions.

ISBN

• 0821821318
• 9780821821312

LCCN

• 00029301
• 9780821821312

OCLC

• ocm43648660
• 43648660
• SCSB-9082609

Owning Institutions

Princeton University Library