Algebra : A Teaching and Source Book / by Ernest Shult, David Surowski

By:

Shult, Ernest [aut]

Contributor(s):

Surowski, David [oth]

Resource type: Ressourcentyp: Buch (Online)Book (Online)Language: English Series: SpringerLink Bücher | Springer eBook Collection Mathematics and StatisticsPublisher: Cham : Springer, 2015Description: Online-Ressource (XXII, 539 p. 6 illus, online resource)ISBN:

9783319197340

Subject(s):

Additional physical formats: 9783319197333 | Druckausg.: Algebra. Cham : Springer, 2015. XXII, 539 S.MSC: MSC: *00A05 | 12-01 | 13-01 | 20-01LOC classification:

QA251.5

DOI: DOI: 10.1007/978-3-319-19734-0Online resources:

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 studentPPN: PPN: 1657495191Package identifier: Produktsigel: ZDB-2-SEB | ZDB-2-SMA | ZDB-2-SXMS

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