Algebras, Lattices, Varieties: Volume I
About this Title
Ralph N. McKenzie, Vanderbilt University, Nashville, TN, George F. McNulty, University of South Carolina, Columbia, SC and Walter F. Taylor, University of Colorado, Boulder, CO
Publication: AMS Chelsea Publishing
Publication Year: 1987; Volume 383
ISBNs: 978-1-4704-4295-8 (print); 978-1-4704-4719-9 (online)
This book presents the foundations of a general theory of algebras. Often called “universal algebra”, this theory provides a common framework for all algebraic systems, including groups, rings, modules, fields, and lattices. Each chapter is replete with useful illustrations and exercises that solidify the reader's understanding.
The book begins by developing the main concepts and working tools of algebras and lattices, and continues with examples of classical algebraic systems like groups, semigroups, monoids, and categories. The essence of the book lies in Chapter 4, which provides not only basic concepts and results of general algebra, but also the perspectives and intuitions shared by practitioners of the field. The book finishes with a study of possible uniqueness of factorizations of an algebra into a direct product of directly indecomposable algebras.
There is enough material in this text for a two semester course sequence, but a one semester course could also focus primarily on Chapter 4, with additional topics selected from throughout the text.
Graduate students and researchers interested in algebra and its applications to lattices, logic, and category theory.
Table of Contents
- Chapter 1. Basic Concepts
- Chapter 2. Lattices
- Chapter 3. Unary and Binary Operations
- Chapter 4. Fundamental Algebraic Results
- Chapter 5. Unique Factorization