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" Taming wild extensions : "
Lindsay N. Childs.
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BL
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| Record Number
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637135
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| Doc. No
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dltt
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| Main Entry
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Childs, Lindsay.
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| Title & Author
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Taming wild extensions : : Hopf algebras and local Galois module theory /\ Lindsay N. Childs.
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| Publication Statement
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Providence, R.I. :: American Mathematical Society,, c2000.
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| Series Statement
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Mathematical surveys and monographs,; v. 80
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| Page. NO
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viii, 215 p. ;; 27 cm.
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| ISBN
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0821821318 (alk. paper)
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: 9780821821312 (alk. paper)
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| Bibliographies/Indexes
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Includes bibliographical references (p. 205-211) and index.
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| Contents
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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.
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| Subject
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Hopf algebras.
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Galois modules (Algebra)
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Field extensions (Mathematics)
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| LC Classification
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QA613.8.C48 2000
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