Basic Notions of Algebra
From the reviews: "This is one of the few mathematical books, the reviewer has read from cover to cover ... The main merit is that nearly on every page you will find some unexpected insights..." Zentralblatt für Mathematik und Ihre Grenzgebiete, 1991 "...which I read like a novel and...
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| Format: | eBook |
| Language: | English |
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Berlin, Heidelberg
Springer Berlin Heidelberg
2005, 2005
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| Edition: | 1st ed. 2005 |
| Series: | Encyclopaedia of Mathematical Sciences
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| Collection: | Springer eBooks 2005- - Collection details see MPG.ReNa |
Table of Contents:
- What is Algebra?
- Fields
- Commutative Rings
- Homomorphisms and Ideals
- Modules
- Algebraic Aspects of Dimension
- The Algebraic View of Infinitesimal Notions
- Noncommutative Rings
- Modules over Noncommutative Rings
- Semisimple Modules and Rings
- Division Algebras of Finite Rank
- The Notion of a Group
- Examples of Groups: Finite Groups
- Examples of Groups: Infinite Discrete Groups
- Examples of Groups: Lie Groups and Algebraic Groups
- General Results of Group Theory
- Group Representations
- Some Applications of Groups
- Lie Algebras and Nonassociative Algebra
- Categories
- Homological Algebra
- K-theory