Introduction to the Theory of Abstract Algebras
eBook - ePub

Introduction to the Theory of Abstract Algebras

Richard S Pierce

Share book
  1. 160 pages
  2. English
  3. ePUB (mobile friendly)
  4. Available on iOS & Android
eBook - ePub

Introduction to the Theory of Abstract Algebras

Richard S Pierce

Book details
Book preview
Table of contents

About This Book

Intended for beginning graduate-level courses, this text introduces various aspects of the theory of abstract algebra. The book is also suitable as independent reading for interested students at that level as well as a primary source for a one-semester course that an instructor may supplement to expand to a full year. Author Richard S. Pierce, a Professor of Mathematics at Seattle's University of Washington, places considerable emphasis on applications of the theory and focuses particularly on lattice theory.
After a preliminary review of set theory, the treatment presents the basic definitions of the theory of abstract algebras. Each of the next four chapters focuses on a major theme of universal algebra: subdirect decompositions, direct decompositions, free algebras, and varieties of algebras. Problems and a Bibliography supplement the text.

Frequently asked questions

How do I cancel my subscription?
Simply head over to the account section in settings and click on “Cancel Subscription” - it’s as simple as that. After you cancel, your membership will stay active for the remainder of the time you’ve paid for. Learn more here.
Can/how do I download books?
At the moment all of our mobile-responsive ePub books are available to download via the app. Most of our PDFs are also available to download and we're working on making the final remaining ones downloadable now. Learn more here.
What is the difference between the pricing plans?
Both plans give you full access to the library and all of Perlego’s features. The only differences are the price and subscription period: With the annual plan you’ll save around 30% compared to 12 months on the monthly plan.
What is Perlego?
We are an online textbook subscription service, where you can get access to an entire online library for less than the price of a single book per month. With over 1 million books across 1000+ topics, we’ve got you covered! Learn more here.
Do you support text-to-speech?
Look out for the read-aloud symbol on your next book to see if you can listen to it. The read-aloud tool reads text aloud for you, highlighting the text as it is being read. You can pause it, speed it up and slow it down. Learn more here.
Is Introduction to the Theory of Abstract Algebras an online PDF/ePUB?
Yes, you can access Introduction to the Theory of Abstract Algebras by Richard S Pierce in PDF and/or ePUB format, as well as other popular books in Matematica & Algebra astratta. We have over one million books available in our catalogue for you to explore.


Basic Concepts
1. Algebras and Relational Systems
The purpose of this section is to introduce the principal object of interest in this book, the notion of an abstract algebra.
1.1 DEFINITION. Let A be a set, and suppose that τ is an ordinal number. A τ-ary partial operation on A is a partial mapping of Aτ to A. That is, F is a τ-ary partial operation if F maps D Aτ to A. If
(F) = Aτ, then F is called a τ-ary operation on A.
1.2 EXAMPLES. (a) τ = 0. A zero-ary partial operation is either the empty set or it is a mapping from A0 = {ø} = {0} into A. In the latter case, it is an operation. Thus, the effect of a zero-ary operation on A is to specify an element of A, and it is common practice to denote a zero-ary operation by listing the element that it selects.
(b) τ = 1. A unary partial operation on A is essentially a mapping from a subset of A to A, since A1 can be identified with A by the correspondence aa(0).
(c) τ = 2. A binary partial operation on A corresponds to a mapping from a subset A × A to A when the natural identification a
a(0), a(1)
is made between A2 and A × A. Examples of such binary operations are common. For instance, the multiplication and addition operations in a ring are binary. Frequently, composition...

Table of contents