Algebraic Systems

Paperback (Softcover reprint of the original 1st ed. 1973)
$111.03 price
(Save 13%)$129.00 List Price
Other sellers (Paperback)
  • All (4) from $79.70   
  • New (4) from $79.70   
Sending request ...

Product Details

  • ISBN-13: 9783642653766
  • Publisher: Springer Berlin Heidelberg
  • Publication date: 7/31/2012
  • Series: Grundlehren der mathematischen Wissenschaften Series , #192
  • Edition description: Softcover reprint of the original 1st ed. 1973
  • Edition number: 1
  • Pages: 336
  • Product dimensions: 6.14 (w) x 9.21 (h) x 0.70 (d)

Table of Contents

I General Concepts.- 1. Relations and Mappings.- 1.1 Sets.- 1.2 Relations.- 1.3 Mappings.- 1.4 Equivalence Relations.- 1.5 Partial and Linear Orderings.- 1.6 Multivalued and Partial Mappings.- 1.7 Cardinal and Ordinal Numbers.- Problems and Complements.- 2. Models and Algebras.- 2.1 n-ary Relations and Functions.- 2.2 Algebraic Systems.- 2.3 Subsystems. Generating Sets.- 2.4 Congruences.- 2.5 Direct Products.- 2 6 Operations on Cardinal and Ordinal Numbers.- Problems and Complements.- II Classical Algebras.- 3. Groupoids and Groups.- 3.1 Groupoids and Semigroups.- 3.2 Quasigroups and Loops.- 3.3 Groups.- Problems and Complements.- 4. Rings and Fields.- 4.1 Rings.- 4.2 Algebraically Closed Fields.- 4.3 Alternative Skew Fields.- 4.4 Linear Algebras.- Problems and Complements.- 5. Lattices (Structures).- 5.1 Lattices.- 5.2 Modular and Distributive Lattices. Boolean Algebras.- III First and Second-Order Languages.- 6. Syntax and Semantics.- 6.1 Terms.- 6.2 Formulas.- 6.3 Second-Order Properties.- 6.4 Elementary Theories and Axiomatic Classes.- Problems and Complements.- 7. Classification of Formulas.- 7.1—-Formulas and—-Formulas.- 7.2 Universall Axiomatic Subclasses.- 7.3—?-Formulas and—?-Formulas.- 7.4 Positive Formulas.- 7.5 Multiplicatively Stable Formulas.- IV Products and Complete Classes.- 8. Filters and Filtered Products.- 8.1 Filters and Ultrafilters.- 8.2 Ultraproducts.- 8.3 Applications of Ultraproducts.- 8.4 Conditionally Filtered Formulas.- 8.5 Cardinality of Ultraproducts.- 8.6 Regular Products.- Problems and Complements.- 9. Indistinguishability and Elementary Embedding.- 9 1 Elementary Embedding.- 9.2 Elementary Subsystems.- 10. Completeness and Model Completeness.- 10.1 Complete Systems of Formulas.- 10.2 Model Completeness.- Problems and Complements.- V Quasivarieties.- 11. General Properties.- 11.1 Characteristic Properties.- 11.2 Defining Relations.- 11 3 Replicas.- Problems and Complements.- 12. Free Systems and Free Compositions.- 12.1 Free Compositions.- 12 2 Independent Elements and Free Systems.- 12.3 Amalgamated Compositions.- Problems and Complements.- VI Varieties.- 13. General Properties.- 13 1 Structural Characteristics.- 13.2 Ranks of Varieties.- 13.3 Varieties of Unoids.- Problems and Complements.- 14. Primitive Closures.- 14 1 Generating Systems.- 14.2 The Lattice of Varieties.- 14.3 Minimal Varieties and Quasivarieties.- Problems and Complements.- Name Index.
Read More Show Less

Customer Reviews

Be the first to write a review
( 0 )
Rating Distribution

5 Star


4 Star


3 Star


2 Star


1 Star


Your Rating:

Your Name: Create a Pen Name or

Barnes & Review Rules

Our reader reviews allow you to share your comments on titles you liked, or didn't, with others. By submitting an online review, you are representing to Barnes & that all information contained in your review is original and accurate in all respects, and that the submission of such content by you and the posting of such content by Barnes & does not and will not violate the rights of any third party. Please follow the rules below to help ensure that your review can be posted.

Reviews by Our Customers Under the Age of 13

We highly value and respect everyone's opinion concerning the titles we offer. However, we cannot allow persons under the age of 13 to have accounts at or to post customer reviews. Please see our Terms of Use for more details.

What to exclude from your review:

Please do not write about reviews, commentary, or information posted on the product page. If you see any errors in the information on the product page, please send us an email.

Reviews should not contain any of the following:

  • - HTML tags, profanity, obscenities, vulgarities, or comments that defame anyone
  • - Time-sensitive information such as tour dates, signings, lectures, etc.
  • - Single-word reviews. Other people will read your review to discover why you liked or didn't like the title. Be descriptive.
  • - Comments focusing on the author or that may ruin the ending for others
  • - Phone numbers, addresses, URLs
  • - Pricing and availability information or alternative ordering information
  • - Advertisements or commercial solicitation


  • - By submitting a review, you grant to Barnes & and its sublicensees the royalty-free, perpetual, irrevocable right and license to use the review in accordance with the Barnes & Terms of Use.
  • - Barnes & reserves the right not to post any review -- particularly those that do not follow the terms and conditions of these Rules. Barnes & also reserves the right to remove any review at any time without notice.
  • - See Terms of Use for other conditions and disclaimers.
Search for Products You'd Like to Recommend

Recommend other products that relate to your review. Just search for them below and share!

Create a Pen Name

Your Pen Name is your unique identity on It will appear on the reviews you write and other website activities. Your Pen Name cannot be edited, changed or deleted once submitted.

Your Pen Name can be any combination of alphanumeric characters (plus - and _), and must be at least two characters long.

Continue Anonymously

    If you find inappropriate content, please report it to Barnes & Noble
    Why is this product inappropriate?
    Comments (optional)