Algebra: A Teaching and Source Book
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Editura: Springer
Limba: Engleza
Nr. pagini: 564
Coperta: Paperback
Dimensiuni: 15.5 x 3.3 x 23.5 cm
An aparitie: 2015
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.
Springer
An aparitie | 2015 |
Autor | Ernest Shult , David Surowski |
Dimensiuni | 15.5 x 3.3 x 23.5 cm |
Editura | Springer |
Format | Paperback |
ISBN | 9783319197333 |
Limba | Engleza |
Nr pag | 564 |
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