• ВХОД

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    Полное описание

    Underwood, R. G. An Introduction to Hopf Algebras : монография / by Robert G. Underwood. - New York, NY : Springer, 2011. - on-line. - URL: http://dx.doi.org/10.1007/978-0-387-72766-0. - Загл. с экрана. - ISBN 978-0-387-72766-0. - Текст : электронный.
    Содержание:
    Preface -- Some Notation -- 1. The Spectrum of a Ring.-2. The Zariski Topology on the Spectrum.-3. Representable Group Functors.-4. Hopf Algebras. -5. Larson Orders.-6. Formal Group Hopf Orders.-7. Hopf Orders in KC_p.-8. Hopf Orders in KC_p

    ГРНТИ УДК
    27.17.19512.552

    Рубрики:
    mathematics
    algebra
    commutative algebra
    commutative rings
    group theory
    mathematics
    algebra
    commutative Rings and Algebras
    group Theory and Generalizations

    Аннотация: The study of Hopf algebras spans many fields in mathematics including topology, algebraic geometry, algebraic number theory, Galois module theory, cohomology of groups, and formal groups and has wide-ranging  connections to fields from theoretical physics to computer science. This text is unique in making this engaging subject accessible to advanced graduate and beginning graduate students and focuses on applications of Hopf algebras to algebraic number theory and Galois  module theory, providing a smooth transition from modern algebra to Hopf algebras. After providing an introduction to the spectrum of a ring and the Zariski topology, the text treats presheaves, sheaves, and representable group functors.  In this way the student transitions smoothly from basic algebraic geometry to Hopf algebras.  The importance of Hopf orders is underscored with applications to algebraic number theory, Galois module theory and the theory of formal groups. By the end of the book, readers will be familiar with established results in the field and ready to pose research questions of their own. An exercise set is included in each of twelve chapters with questions ranging in difficulty. Open problems and research questions are presented in the last chapter. Prerequisites include an understanding of the  material on groups, rings, and fields normally covered in a basic course in modern algebra.

    http://dx.doi.org/10.1007/978-0-387-72766-0


    Держатели документа:
    Государственная публичная научно-техническая библиотека России : 123298, г. Москва, ул. 3-я Хорошевская, д. 17 (Шифр в БД-источнике (KATBW): -063735239)

    Шифр в сводном ЭК: cc01ad2d2066e94ca3b4e5620c17a264



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