Algebra

1. Front Matter

   Pages i-xi

   PDF

2. Set theory

   • L. E. Sigler

   Pages 1-30

3. Rings: Basic theory

   • L. E. Sigler

   Pages 31-66

4. Rings: Natural numbers and integers

   • L. E. Sigler

   Pages 67-91

5. Rings: Applications of the integers

   • L. E. Sigler

   Pages 92-117

6. Rings: Polynomials and factorization

   • L. E. Sigler

   Pages 118-156

7. Linear algebra: Modules

   • L. E. Sigler

   Pages 157-226

8. Linear algebra: The module of morphisms

   • L. E. Sigler

   Pages 227-296

9. Abstract systems

   • L. E. Sigler

   Pages 297-322

10. Monoids and groups

    • L. E. Sigler

    Pages 323-362

11. Linear algebra: Modules over principal domains and similarity

    • L. E. Sigler

    Pages 363-407

12. Back Matter

    Pages 409-419

    PDF

There is no one best way for an undergraduate student to learn elementary algebra. Some kinds of presentations will please some learners and will disenchant others. This text presents elementary algebra organized accord­ ing to some principles of universal algebra. Many students find such a presentation of algebra appealing and easier to comprehend. The approach emphasizes the similarities and common concepts of the many algebraic structures. Such an approach to learning algebra must necessarily have its formal aspects, but we have tried in this presentation not to make abstraction a goal in itself. We have made great efforts to render the algebraic concepts intuitive and understandable. We have not hesitated to deviate from the form of the text when we feel it advisable for the learner. Often the presenta­ tions are concrete and may be regarded by some as out of fashion. How to present a particular topic is a subjective one dictated by the author's estima­ tion of what the student can best handle at this level. We do strive for consistent unifying terminology and notation. This means abandoning terms peculiar to one branch of algebra when there is available a more general term applicable to all of algebra. We hope that this text is readable by the student as well as the instructor. It is a goal of ours to free the instructor for more creative endeavors than reading the text to the students.

• algebra
• field
• linear algebra
• matrices
• matrix

• Department of Mathematics, Bucknell University, Lewisburg, USA

  L. E. Sigler

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