Algebra: A Teaching And Source Book
by Ernest Shult /
2015 / English / PDF
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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 JordanHolder 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 idealsin 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.
