TY - BOOK ID - 4865415 TI - Algebra : A Teaching and Source Book AU - Shult, Ernest. AU - Surowski, David. PY - 2015 SN - 9783319197340 3319197339 9783319197333 3319197347 PB - Cham : Springer International Publishing : Imprint: Springer, DB - UniCat KW - Mathematics. KW - Associative Rings and Algebras. KW - Group Theory and Generalizations. KW - Field Theory and Polynomials. KW - Algebra. KW - Field theory (Physics). KW - Group theory. KW - Mathématiques KW - Algèbre KW - Champs, Théorie des (Physique) KW - Groupes, Théorie des KW - Algebra KW - Mathematics KW - Physical Sciences & Mathematics KW - Théorie des groupes KW - Associative rings. KW - Rings (Algebra). KW - Groups, Theory of KW - Substitutions (Mathematics) KW - Classical field theory KW - Continuum physics KW - Physics KW - Continuum mechanics KW - Mathematical analysis KW - Algebraic rings KW - Ring theory KW - Algebraic fields KW - Rings (Algebra) KW - Field theory (Physics) UR - https://www.unicat.be/uniCat?func=search&query=sysid:4865415 AB - 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. ER -