Includes bibliographical references (p. 205-211) and index.
CONTENTS NOTE
Text of Note
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.