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This text aims to provide graduate students with a self-contained
introduction to topics that are at the forefront of modern algebra,
namely, coalgebras, bialgebras and Hopf algebras. The last chapter
(Chapter 4) discusses several applications of Hopf algebras, some
of which are further developed in the author's 2011 publication, An
Introduction to Hopf Algebras. The book may be used as the main
text or as a supplementary text for a graduate algebra course.
Prerequisites for this text include standard material on groups,
rings, modules, algebraic extension fields, finite fields and
linearly recursive sequences. The book consists of four chapters.
Chapter 1 introduces algebras and coalgebras over a field K;
Chapter 2 treats bialgebras; Chapter 3 discusses Hopf algebras and
Chapter 4 consists of three applications of Hopf algebras. Each
chapter begins with a short overview and ends with a collection of
exercises which are designed to review and reinforce the material.
Exercises range from straightforward applications of the theory to
problems that are devised to challenge the reader. Questions for
further study are provided after selected exercises. Most proofs
are given in detail, though a few proofs are omitted since they are
beyond the scope of this book.
Only book on Hopf algebras aimed at advanced undergraduates
Only book on Hopf algebras aimed at advanced undergraduates
The purpose of this book is to provide a concise yet detailed
account of fundamental concepts in modern algebra. The target
audience for this book is first-year graduate students in
mathematics, though the first two chapters are probably accessible
to well-prepared undergraduates. The book covers a broad range of
topics in modern algebra and includes chapters on groups, rings,
modules, algebraic extension fields, and finite fields. Each
chapter begins with an overview which provides a road map for the
reader showing what material will be covered. At the end of each
chapter we collect exercises which review and reinforce the
material in the corresponding sections. These exercises range from
straightforward applications of the material to problems designed
to challenge the reader. We also include a list of 'Questions for
Further Study' which pose problems suitable for master's degree
research projects.
The purpose of this book is to provide a concise yet detailed
account of fundamental concepts in modern algebra. The target
audience for this book is first-year graduate students in
mathematics, though the first two chapters are probably accessible
to well-prepared undergraduates. The book covers a broad range of
topics in modern algebra and includes chapters on groups, rings,
modules, algebraic extension fields, and finite fields. Each
chapter begins with an overview which provides a road map for the
reader showing what material will be covered. At the end of each
chapter we collect exercises which review and reinforce the
material in the corresponding sections. These exercises range from
straightforward applications of the material to problems designed
to challenge the reader. We also include a list of 'Questions for
Further Study' which pose problems suitable for master's degree
research projects.
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