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Author: Susan Montgomery
Publisher: American Mathematical Soc.
ISBN: 0821850466
Category : Mathematics
Languages : en
Pages : 290
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Book Description
Ring theorists and researchers in invariant theory and operator algebra met at Bowdoin for the 1984 AMS-IMS-SIAM Joint Summer Research Conference to exchange ideas about group actions on rings. This work discusses topics common to the three fields, including: $K$-theory, dual actions, semi-invariants and crossed products.
Author: Susan Montgomery
Publisher: American Mathematical Soc.
ISBN: 0821850466
Category : Mathematics
Languages : en
Pages : 290
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Book Description
Ring theorists and researchers in invariant theory and operator algebra met at Bowdoin for the 1984 AMS-IMS-SIAM Joint Summer Research Conference to exchange ideas about group actions on rings. This work discusses topics common to the three fields, including: $K$-theory, dual actions, semi-invariants and crossed products.
Author: Shahriar Shahriar
Publisher: American Mathematical Soc.
ISBN: 1470428490
Category : Mathematics
Languages : en
Pages : 698
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Book Description
This text—based on the author's popular courses at Pomona College—provides a readable, student-friendly, and somewhat sophisticated introduction to abstract algebra. It is aimed at sophomore or junior undergraduates who are seeing the material for the first time. In addition to the usual definitions and theorems, there is ample discussion to help students build intuition and learn how to think about the abstract concepts. The book has over 1300 exercises and mini-projects of varying degrees of difficulty, and, to facilitate active learning and self-study, hints and short answers for many of the problems are provided. There are full solutions to over 100 problems in order to augment the text and to model the writing of solutions. Lattice diagrams are used throughout to visually demonstrate results and proof techniques. The book covers groups, rings, and fields. In group theory, group actions are the unifying theme and are introduced early. Ring theory is motivated by what is needed for solving Diophantine equations, and, in field theory, Galois theory and the solvability of polynomials take center stage. In each area, the text goes deep enough to demonstrate the power of abstract thinking and to convince the reader that the subject is full of unexpected results.
Author: Susan Montgomery
Publisher: American Mathematical Soc.
ISBN: 0821807382
Category : Mathematics
Languages : en
Pages : 258
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Book Description
The last ten years have seen a number of significant advances in Hopf algebras. The best known is the introduction of quantum groups, which are Hopf algebras that arose in mathematical physics and now have connections to many areas of mathematics. In addition, several conjectures of Kaplansky have been solved, the most striking of which is a kind of Lagrange's theorem for Hopf algebras. Work on actions of Hopf algebras has unified earlier results on group actions, actions of Lie algebras, and graded algebras. This book brings together many of these recent developments from the viewpoint of the algebraic structure of Hopf algebras and their actions and coactions. Quantum groups are treated as an important example, rather than as an end in themselves. The two introductory chapters review definitions and basic facts; otherwise, most of the material has not previously appeared in book form. Providing an accessible introduction to Hopf algebras, this book would make an excellent graduate textbook for a course in Hopf algebras or an introduction to quantum groups.
Author: César Polcino Milies
Publisher: Springer Science & Business Media
ISBN: 9781402002380
Category : Mathematics
Languages : en
Pages : 394
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Book Description
to Group Rings by Cesar Polcino Milies Instituto de Matematica e Estatistica, Universidade de sao Paulo, sao Paulo, Brasil and Sudarshan K. Sehgal Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton. Canada SPRINGER-SCIENCE+BUSINESS MEDIA, B.V. A c.I.P. Catalogue record for this book is available from the Library of Congress. ISBN 978-1-4020-0239-7 ISBN 978-94-010-0405-3 (eBook) DOI 10.1007/978-94-010-0405-3 Printed an acid-free paper AII Rights Reserved (c) 2002 Springer Science+Business Media Dordrecht Originally published by Kluwer Academic Publishers in 2002 Softcover reprint ofthe hardcover Ist edition 2002 No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical, inc1uding photocopying, recording Of by any information storage and retrieval system, without written permis sion from the copyright owner. Contents Preface ix 1 Groups 1 1.1 Basic Concepts . . . . . . . . . . . . 1 1.2 Homomorphisms and Factor Groups 10 1.3 Abelian Groups . 18 1.4 Group Actions, p-groups and Sylow Subgroups 21 1.5 Solvable and Nilpotent Groups 27 1.6 FC Groups .
Author: A. Giambruno
Publisher: American Mathematical Soc.
ISBN: 0821847716
Category : Mathematics
Languages : en
Pages : 283
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Book Description
Represents the proceedings of the conference on Groups, Rings and Group Rings, held July 28 - August 2, 2008, in Ubatuba, Brazil. This title contains results in active research areas in the theory of groups, group rings and algebras (including noncommutative rings), polynomial identities, Lie algebras and superalgebras.
Author: Nathan Carter
Publisher: American Mathematical Soc.
ISBN: 1470464330
Category : Education
Languages : en
Pages : 295
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Book Description
Recipient of the Mathematical Association of America's Beckenbach Book Prize in 2012! Group theory is the branch of mathematics that studies symmetry, found in crystals, art, architecture, music and many other contexts, but its beauty is lost on students when it is taught in a technical style that is difficult to understand. Visual Group Theory assumes only a high school mathematics background and covers a typical undergraduate course in group theory from a thoroughly visual perspective. The more than 300 illustrations in Visual Group Theory bring groups, subgroups, homomorphisms, products, and quotients into clear view. Every topic and theorem is accompanied with a visual demonstration of its meaning and import, from the basics of groups and subgroups through advanced structural concepts such as semidirect products and Sylow theory.
Author: Bernd Sturmfels
Publisher: Springer Science & Business Media
ISBN: 3211774173
Category : Mathematics
Languages : en
Pages : 202
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Book Description
This book is both an easy-to-read textbook for invariant theory and a challenging research monograph that introduces a new approach to the algorithmic side of invariant theory. Students will find the book an easy introduction to this "classical and new" area of mathematics. Researchers in mathematics, symbolic computation, and computer science will get access to research ideas, hints for applications, outlines and details of algorithms, examples and problems.
Author: Matej Brešar
Publisher: Springer
ISBN: 9783030140526
Category : Mathematics
Languages : en
Pages : 316
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Book Description
This textbook offers an innovative approach to abstract algebra, based on a unified treatment of similar concepts across different algebraic structures. This makes it possible to express the main ideas of algebra more clearly and to avoid unnecessary repetition. The book consists of two parts: The Language of Algebra and Algebra in Action. The unified approach to different algebraic structures is a primary feature of the first part, which discusses the basic notions of algebra at an elementary level. The second part is mathematically more complex, covering topics such as the Sylow theorems, modules over principal ideal domains, and Galois theory. Intended for an undergraduate course or for self-study, the book is written in a readable, conversational style, is rich in examples, and contains over 700 carefully selected exercises.
Author: Stephen Urban Chase
Publisher: American Mathematical Soc.
ISBN: 0821812521
Category : Commutative rings
Languages : en
Pages : 87
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Book Description
Author: Paolo Aluffi
Publisher: American Mathematical Soc.
ISBN: 147046571X
Category : Education
Languages : en
Pages : 713
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Book Description
Algebra: Chapter 0 is a self-contained introduction to the main topics of algebra, suitable for a first sequence on the subject at the beginning graduate or upper undergraduate level. The primary distinguishing feature of the book, compared to standard textbooks in algebra, is the early introduction of categories, used as a unifying theme in the presentation of the main topics. A second feature consists of an emphasis on homological algebra: basic notions on complexes are presented as soon as modules have been introduced, and an extensive last chapter on homological algebra can form the basis for a follow-up introductory course on the subject. Approximately 1,000 exercises both provide adequate practice to consolidate the understanding of the main body of the text and offer the opportunity to explore many other topics, including applications to number theory and algebraic geometry. This will allow instructors to adapt the textbook to their specific choice of topics and provide the independent reader with a richer exposure to algebra. Many exercises include substantial hints, and navigation of the topics is facilitated by an extensive index and by hundreds of cross-references.
