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)
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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 p2; 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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1.

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)
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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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Childs, Lindsay N.
ISBN 10: 0821821318 ISBN 13: 9780821821312
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Descripción Estado de conservación: New. Depending on your location, this item may ship from the US or UK. Nº de ref. de la librería 97808218213120000000

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Lindsay N. Childs
Editorial: American Mathematical Society, United States (2000)
ISBN 10: 0821821318 ISBN 13: 9780821821312
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The Book Depository
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Descripción American Mathematical Society, United States, 2000. Hardback. Estado de conservación: New. 260 x 178 mm. 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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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 US
(London, Reino Unido)
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Descripción American Mathematical Society, United States, 2000. Hardback. Estado de conservación: New. 260 x 178 mm. 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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Lindsay N. Childs
Editorial: American Mathematical Society
ISBN 10: 0821821318 ISBN 13: 9780821821312
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THE SAINT BOOKSTORE
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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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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
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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
Editorial: American Mathematical Society (2000)
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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
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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
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Descripción 2000. Hardcover. Estado de conservación: New. 230mm x 19mm x 260mm. Hardcover. 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 previo.Shipping may be from our Sydney, NSW warehouse or from our UK or US warehouse, depending on stock availability. 215 pages. 0.624. Nº de ref. de la librería 9780821821312

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Lindsay N. Childs
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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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