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Algebra : A Teaching and Source Book / by Ernest Shult, David Surowski.
Springer Nature - Springer Mathematics and Statistics eBooks 2015 English International Available online
View online- Format:
- Book
- Author/Creator:
- Shult, Ernest., Author.
- Surowski, David., Author.
- Language:
- English
- Subjects (All):
- Associative rings.
- Rings (Algebra).
- Group theory.
- Algebra.
- Field theory (Physics).
- Associative Rings and Algebras.
- Group Theory and Generalizations.
- Field Theory and Polynomials.
- Local Subjects:
- Associative Rings and Algebras.
- Group Theory and Generalizations.
- Field Theory and Polynomials.
- Algebra.
- Physical Description:
- 1 online resource (XXII, 539 p. 6 illus.)
- Edition:
- 1st ed. 2015.
- Place of Publication:
- Cham : Springer International Publishing : Imprint: Springer, 2015.
- Language Note:
- English
- Summary:
- This book presents a graduate-level course on modern algebra. It can be used as a teaching book – owing to the copious exercises – and as a source book for those who wish to use the major theorems of algebra. The course begins with the basic combinatorial principles of algebra: posets, chain conditions, Galois connections, and dependence theories. Here, the general Jordan–Holder Theorem becomes a theorem on interval measures of certain lower semilattices. This is followed by basic courses on groups, rings and modules; the arithmetic of integral domains; fields; the categorical point of view; and tensor products. Beginning with introductory concepts and examples, each chapter proceeds gradually towards its more complex theorems. Proofs progress step-by-step from first principles. Many interesting results reside in the exercises, for example, the proof that ideals in a Dedekind domain are generated by at most two elements. The emphasis throughout is on real understanding as opposed to memorizing a catechism and so some chapters offer curiosity-driven appendices for the self-motivated student.
- Contents:
- Basics
- Basic Combinatorial Principles of Algebra
- Review of Elementary Group Properties
- Permutation Groups and Group Actions
- Normal Structure of Groups
- Generation in Groups
- Elementary Properties of Rings
- Elementary properties of Modules
- The Arithmetic of Integral Domains
- Principal Ideal Domains and Their Modules
- Theory of Fields
- Semiprime Rings
- Tensor Products.
- Notes:
- Bibliographic Level Mode of Issuance: Monograph
- Includes bibliographical references and index.
- Description based on publisher supplied metadata and other sources.
- ISBN:
- 3-319-19734-7
- OCLC:
- 1066188069
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