Taming Wild Extensions: Hopf Algebras and Local Galois Module Theory (Mathematical Surveys and Monographs)

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9780821821312: Taming Wild Extensions: Hopf Algebras and Local Galois Module Theory (Mathematical Surveys and Monographs)

This book studies Hopf algebras over valuation rings of local fields and their application to the theory of wildly ramified extensions of local fields. The results, not previously published in book form, show that Hopf algebras play a natural role in local Galois module theory. Included in this work are expositions of short exact sequences of Hopf algebras; Hopf Galois structures on separable field extensions; a generalization of Noether's theorem on the Galois module structure of tamely ramified extensions of local fields to wild extensions acted on by Hopf algebras; connections between tameness and being Galois for algebras acted on by a Hopf algebra; constructions by Larson and Greither of Hopf orders over valuation rings; ramification criteria of Byott and Greither for the associated order of the valuation ring of an extension of local fields to be Hopf order; the Galois module structure of wildly ramified cyclic extensions of local fields of degree $p$ and $p^2$; and Kummer theory of formal groups. Beyond a general background in graduate-level algebra, some chapters assume an acquaintance with some algebraic number theory. From there, this exposition serves as an excellent resource and motivation for further work in the field.

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This monograph, authored by a leading expert and main contributor in the field, is very painstakingly written ... The book offers an ideal road of entry into the subject, for everybody with an interest in local Galois module theory or in the theory of Hopf algebras.

Zentralblatt f\"ur Mathematik

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A pleasure to read ... excellent material Mathematical Reviews

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1.

Lindsay N. Childs
Editorial: American Mathematical Society (2000)
ISBN 10: 0821821318 ISBN 13: 9780821821312
Nuevos Tapa dura Cantidad: 2
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Murray Media
(North Miami Beach, FL, Estados Unidos de America)
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Descripción American Mathematical Society, 2000. Hardcover. Estado de conservación: New. Nº de ref. de la librería P110821821318

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2.

Lindsay N. Childs
Editorial: American Mathematical Society, United States (2000)
ISBN 10: 0821821318 ISBN 13: 9780821821312
Nuevos Tapa dura Cantidad: 1
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The Book Depository
(London, Reino Unido)
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Descripción American Mathematical Society, United States, 2000. Hardback. Estado de conservación: New. Language: English . Brand New Book. This book studies Hopf algebras over valuation rings of local fields and their application to the theory of wildly ramified extensions of local fields. The results, not previously published in book form, show that Hopf algebras play a natural role in local Galois module theory.Included in this work are expositions of short exact sequences of Hopf algebras; Hopf Galois structures on separable field extensions; a generalization of Noether s theorem on the Galois module structure of tamely ramified extensions of local fields to wild extensions acted on by Hopf algebras; connections between tameness and being Galois for algebras acted on by a Hopf algebra; constructions by Larson and Greither of Hopf orders over valuation rings; ramification criteria of Byott and Greither for the associated order of the valuation ring of an extension of local fields to be Hopf order; the Galois module structure of wildly ramified cyclic extensions of local fields of degree $p$ and $p^2$; and, Kummer theory of formal groups. Beyond a general background in graduate-level algebra, some chapters assume an acquaintance with some algebraic number theory.From there, this exposition serves as an excellent resource and motivation for further work in the field. Nº de ref. de la librería AAN9780821821312

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3.

Lindsay N. Childs
Editorial: American Mathematical Society, United States (2000)
ISBN 10: 0821821318 ISBN 13: 9780821821312
Nuevos Tapa dura Cantidad: 1
Librería
The Book Depository US
(London, Reino Unido)
Valoración
[?]

Descripción American Mathematical Society, United States, 2000. Hardback. Estado de conservación: New. Language: English . Brand New Book. This book studies Hopf algebras over valuation rings of local fields and their application to the theory of wildly ramified extensions of local fields. The results, not previously published in book form, show that Hopf algebras play a natural role in local Galois module theory.Included in this work are expositions of short exact sequences of Hopf algebras; Hopf Galois structures on separable field extensions; a generalization of Noether s theorem on the Galois module structure of tamely ramified extensions of local fields to wild extensions acted on by Hopf algebras; connections between tameness and being Galois for algebras acted on by a Hopf algebra; constructions by Larson and Greither of Hopf orders over valuation rings; ramification criteria of Byott and Greither for the associated order of the valuation ring of an extension of local fields to be Hopf order; the Galois module structure of wildly ramified cyclic extensions of local fields of degree $p$ and $p^2$; and, Kummer theory of formal groups. Beyond a general background in graduate-level algebra, some chapters assume an acquaintance with some algebraic number theory.From there, this exposition serves as an excellent resource and motivation for further work in the field. Nº de ref. de la librería AAN9780821821312

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4.

Lindsay N. Childs
Editorial: American Mathematical Society
ISBN 10: 0821821318 ISBN 13: 9780821821312
Nuevos Tapa dura Cantidad: 1
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THE SAINT BOOKSTORE
(Southport, Reino Unido)
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Descripción American Mathematical Society. Hardback. Estado de conservación: new. BRAND NEW, Taming Wild Extensions: Hopf Algebras and Local Galois Module Theory, Lindsay N. Childs, This book studies Hopf algebras over valuation rings of local fields and their application to the theory of wildly ramified extensions of local fields. The results, not previously published in book form, show that Hopf algebras play a natural role in local Galois module theory.Included in this work are expositions of short exact sequences of Hopf algebras; Hopf Galois structures on separable field extensions; a generalization of Noether's theorem on the Galois module structure of tamely ramified extensions of local fields to wild extensions acted on by Hopf algebras; connections between tameness and being Galois for algebras acted on by a Hopf algebra; constructions by Larson and Greither of Hopf orders over valuation rings; ramification criteria of Byott and Greither for the associated order of the valuation ring of an extension of local fields to be Hopf order; the Galois module structure of wildly ramified cyclic extensions of local fields of degree $p$ and $p^2$; and, Kummer theory of formal groups. Beyond a general background in graduate-level algebra, some chapters assume an acquaintance with some algebraic number theory. From there, this exposition serves as an excellent resource and motivation for further work in the field. Nº de ref. de la librería B9780821821312

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5.

Lindsay N. Childs
Editorial: American Mathematical Society (2000)
ISBN 10: 0821821318 ISBN 13: 9780821821312
Nuevos Tapa dura Cantidad: > 20
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Sequitur Books
(Boonsboro, MD, Estados Unidos de America)
Valoración
[?]

Descripción American Mathematical Society, 2000. Hardcover. Estado de conservación: New. Brand new. We distribute directly for the publisher. This book studies Hopf algebras over valuation rings of local fields and their application to the theory of wildly ramified extensions of local fields. The results, not previously published in book form, show that Hopf algebras play a natural role in local Galois module theory.Included in this work are expositions of short exact sequences of Hopf algebras; Hopf Galois structures on separable field extensions; a generalization of Noether's theorem on the Galois module structure of tamely ramified extensions of local fields to wild extensions acted on by Hopf algebras; connections between tameness and being Galois for algebras acted on by a Hopf algebra; constructions by Larson and Greither of Hopf orders over valuation rings; ramification criteria of Byott and Greither for the associated order of the valuation ring of an extension of local fields to be Hopf order; the Galois module structure of wildly ramified cyclic extensions of local fields of degree $p$ and $p^2$; and Kummer theory of formal groups.Beyond a general background in graduate-level algebra, some chapters assume an acquaintance with some algebraic number theory. From there, this exposition serves as an excellent resource and motivation for further work in the field. Nº de ref. de la librería 1006240186

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6.

Lindsay N. Childs
Editorial: American Mathematical Society (2000)
ISBN 10: 0821821318 ISBN 13: 9780821821312
Nuevos Tapa dura Cantidad: 1
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Ergodebooks
(RICHMOND, TX, Estados Unidos de America)
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Descripción American Mathematical Society, 2000. Hardcover. Estado de conservación: New. Nº de ref. de la librería DADAX0821821318

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Childs, Lindsay
Editorial: Amer Mathematical Society (2000)
ISBN 10: 0821821318 ISBN 13: 9780821821312
Nuevos Tapa dura Cantidad: 1
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Revaluation Books
(Exeter, Reino Unido)
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Descripción Amer Mathematical Society, 2000. Hardcover. Estado de conservación: Brand New. 215 pages. 10.25x7.50x0.50 inches. In Stock. Nº de ref. de la librería __0821821318

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Lindsay N. Childs
Editorial: American Mathematical Society (2000)
ISBN 10: 0821821318 ISBN 13: 9780821821312
Nuevos Tapa dura Cantidad: 1
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Irish Booksellers
(Rumford, ME, Estados Unidos de America)
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Descripción American Mathematical Society, 2000. Hardcover. Estado de conservación: New. book. Nº de ref. de la librería 0821821318

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Lindsay N. Childs
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Castle Rock
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Descripción Estado de conservación: Brand New. Book Condition: Brand New. Nº de ref. de la librería 97808218213121.0

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