TY - BOOK
AU - Shult,Ernest
AU - Surowski,David
ED - SpringerLink (Online service)
TI - Algebra: A Teaching and Source Book
SN - 9783319197340
AV - QA251.5
U1 - 512.46 23
PY - 2015///
CY - Cham
PB - Springer International Publishing, Imprint: Springer
KW - Mathematics
KW - Algebra
KW - Associative rings
KW - Rings (Algebra)
KW - Field theory (Physics)
KW - Group theory
KW - Associative Rings and Algebras
KW - Group Theory and Generalizations
KW - Field Theory and Polynomials
N1 - 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
N2 - 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
UR - http://dx.doi.org/10.1007/978-3-319-19734-0
ER -