Post-Modern Algebra

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John Wiley & Sons, Feb 2, 1999 - Mathematics - 370 pages
Advanced algebra in the service of contemporary mathematical research— a unique introduction.

This volume takes an altogether new approach to advanced algebra. Its intriguing title, inspired by the term postmodernism, denotes a departure from van der Waerden's Modern Algebra—a book that has dominated the field for nearly seventy years. Post-Modern Algebra offers a truly up-to-date alternative to the standard approach, explaining topics from an applications-based perspective rather than by abstract principles alone. The book broadens the field of study to include algebraic structures and methods used in current and emerging mathematical research, and describes the powerful yet subtle techniques of universal algebra and category theory. Classical algebraic areas of groups, rings, fields, and vector spaces are bolstered by such topics as ordered sets, monoids, monoid actions, quasigroups, loops, lattices, Boolean algebras, categories, and Heyting algebras. The text features:

  • A clear and concise treatment at an introductory level, tested in university courses.
  • A wealth of exercises illustrating concepts and their practical application.
  • Effective techniques for solving research problems in the real world.
  • Flexibility of presentation, making it easy to tailor material to specific needs.
  • Help with elementary proofs and algebraic notations for students of varying abilities.

    Post-Modern Algebra is an excellent primary or supplementary text for graduate-level algebra courses. It is also an extremely useful resource for professionals and researchers in many areas who must tackle abstract, linear, or universal algebra in the course of their work.

 

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Contents

GROUPS AND QUASIGROUPS
29
Groups and Quasigroups
51
LINEAR ALGEBRA
111
CATEGORIES AND LATTICES
191
Limits and Lattices
213
UNIVERSAL ALGEBRA
281
INDEX
359
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About the author (1999)

JONATHAN D. H. SMITH is Professor of Mathematics at Iowa State University. His research interests comprise algebra, combinatorics, and information theory, with applications in computer science, complex systems, physics, and biology. He has published more than sixty research papers and written or edited six books.

ANNA B. ROMANOWSKA is Professor of Mathematics at Warsaw University of Technology. Her research interests include universal algebra, lattice theory, and logic, with applications in computer science and music theory. She has published fifty-five research papers and written or edited three books.