A Course in Universal Algebra

Sufficiently develops a few themes central to universal algebra to bring the reader to the brink of current research. This text is not intended to be encyclopedic.

**Tag(s):**
Algebra

**Publication date**: 31 Dec 1981

**ISBN-10**:
n/a

**ISBN-13**:
n/a

**Paperback**:
n/a

**Views**: 20,619

A Course in Universal Algebra

Sufficiently develops a few themes central to universal algebra to bring the reader to the brink of current research. This text is not intended to be encyclopedic.

Terms and Conditions:

Book Excerpts:

Universal algebra has enjoyed a particularly explosive growth in the last twenty years (ed: this book was published in 1981), and a student entering the subject now will find a bewildering amount of material to digest.

This text is not intended to be encyclopedic; rather, a few themes central to universal algebra have been developed sufficiently to bring the reader to the brink of current research. The choice of topics most certainly reflects the authors' interests.

Chapter I contains a brief but substantial introduction to lattices. and to the close connection between complete lattices and closure operators. In particular, everything necessary for the subsequent study of congruence lattices is included.

Chapter II develops the most general and fundamental notions of universal algebra these include the results that apply to all types of algebras, such as the homomorphism and isomorphism theorems.

In Chapter III this book shows how neatly two famous results the refutation of Euler's conjecture on orthogonal Latin squares and Kleene's characterization of languages accepted by finite automata can be presented using universal algebra.

Chapter IV starts with a careful development of Boolean algebras, including Stone duality, which is subsequently used in our study of Boolean sheaf representations; however, the cumbersome formulation of general sheaf theory has been replaced by the considerably simpler definition of a Boolean product.

The final chapter gives the reader a leisurely introduction to some basic concepts, tools, and results of model theory. In particular, this book uses the ultraproduct construction to derive the compactness theorem and to prove fundamental preservation theorems. Principal congruence formulas are a favorite model-theoretic tool of universal algebraists, and this book uses them in the study of the sizes of subdirectly irreducible algebras. Next this book proves three general results on the existence of a finite basis for an equational theory. The last topic is semantic embeddings, a popular technique for proving undecidability results. This technique is essentially algebraic in nature, requiring no familiarity whatsoever with the theory of algorithms. (The study of decidability has given surprisingly deep insight into the limitations of Boolean product representations.)

At the end of several sections the reader will find selected references to source material plus state of the art texts or papers relevant to that section, and at the end of the book one finds a brief survey of recent developments and several outstanding problems.

Stanley Burris wrote:(C) S. Burris and H.P. Sankappanavar. All Rights Reserved. This Edition may be copied for personal use.

Book Excerpts:

Universal algebra has enjoyed a particularly explosive growth in the last twenty years (ed: this book was published in 1981), and a student entering the subject now will find a bewildering amount of material to digest.

This text is not intended to be encyclopedic; rather, a few themes central to universal algebra have been developed sufficiently to bring the reader to the brink of current research. The choice of topics most certainly reflects the authors' interests.

Chapter I contains a brief but substantial introduction to lattices. and to the close connection between complete lattices and closure operators. In particular, everything necessary for the subsequent study of congruence lattices is included.

Chapter II develops the most general and fundamental notions of universal algebra these include the results that apply to all types of algebras, such as the homomorphism and isomorphism theorems.

In Chapter III this book shows how neatly two famous results the refutation of Euler's conjecture on orthogonal Latin squares and Kleene's characterization of languages accepted by finite automata can be presented using universal algebra.

Chapter IV starts with a careful development of Boolean algebras, including Stone duality, which is subsequently used in our study of Boolean sheaf representations; however, the cumbersome formulation of general sheaf theory has been replaced by the considerably simpler definition of a Boolean product.

The final chapter gives the reader a leisurely introduction to some basic concepts, tools, and results of model theory. In particular, this book uses the ultraproduct construction to derive the compactness theorem and to prove fundamental preservation theorems. Principal congruence formulas are a favorite model-theoretic tool of universal algebraists, and this book uses them in the study of the sizes of subdirectly irreducible algebras. Next this book proves three general results on the existence of a finite basis for an equational theory. The last topic is semantic embeddings, a popular technique for proving undecidability results. This technique is essentially algebraic in nature, requiring no familiarity whatsoever with the theory of algorithms. (The study of decidability has given surprisingly deep insight into the limitations of Boolean product representations.)

At the end of several sections the reader will find selected references to source material plus state of the art texts or papers relevant to that section, and at the end of the book one finds a brief survey of recent developments and several outstanding problems.

Tweet

About The Author(s)

No information is available for this author.

No information is available for this author.

Book Categories

Computer Science
Introduction to Computer Science
Introduction to Computer Programming
Algorithms and Data Structures
Artificial Intelligence
Computer Vision
Machine Learning
Neural Networks
Game Development and Multimedia
Data Communication and Networks
Coding Theory
Computer Security
Information Security
Cryptography
Information Theory
Computer Organization and Architecture
Operating Systems
Image Processing
Parallel Computing
Concurrent Programming
Relational Database
Document-oriented Database
Data Mining
Big Data
Data Science
Digital Libraries
Compiler Design and Construction
Functional Programming
Logic Programming
Object Oriented Programming
Formal Methods
Software Engineering
Agile Software Development
Information Systems
Geographic Information System (GIS)

Mathematics
Mathematics
Algebra
Abstract Algebra
Linear Algebra
Number Theory
Numerical Methods
Precalculus
Calculus
Differential Equations
Category Theory
Proofs
Discrete Mathematics
Theory of Computation
Graph Theory
Real Analysis
Complex Analysis
Probability
Statistics
Game Theory
Queueing Theory
Operations Research
Computer Aided Mathematics

Supporting Fields
Web Design and Development
Mobile App Design and Development
System Administration
Cloud Computing
Electric Circuits
Embedded System
Signal Processing
Integration and Automation
Network Science
Project Management

Operating System
Programming/Scripting
Ada
Assembly
C / C++
Common Lisp
Forth
Java
JavaScript
Lua
Microsoft .NET
Rexx
Perl
PHP
Python
R
Rebol
Ruby
Scheme
Tcl/Tk

Miscellaneous
Sponsors