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150714s2015 gw | s |||| 0|eng d |
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|a 9783319197340
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7 |
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|a 10.1007/978-3-319-19734-0
|2 doi
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|a (DE-He213)978-3-319-19734-0
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1 |
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|a Shult, Ernest.
|e author.
|4 aut
|4 http://id.loc.gov/vocabulary/relators/aut
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| 245 |
1 |
0 |
|a Algebra
|h [electronic resource] :
|b A Teaching and Source Book /
|c by Ernest Shult, David Surowski.
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| 250 |
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|a 1st ed. 2015.
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| 264 |
|
1 |
|a Cham :
|b Springer International Publishing :
|b Imprint: Springer,
|c 2015.
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| 300 |
|
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|a XXII, 539 p. 6 illus.
|b online resource.
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| 336 |
|
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|a text
|b txt
|2 rdacontent
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|a computer
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|a online resource
|b cr
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| 347 |
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|a text file
|b PDF
|2 rda
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| 490 |
1 |
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|a Springer eBook Collection
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| 505 |
0 |
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|a 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.
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| 520 |
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|a 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.
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| 590 |
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|a Loaded electronically.
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| 590 |
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|a Electronic access restricted to members of the Holy Cross Community.
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| 650 |
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0 |
|a Associative rings.
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| 650 |
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0 |
|a Rings (Algebra).
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| 650 |
|
0 |
|a Group theory.
|
| 650 |
|
0 |
|a Algebra.
|
| 650 |
|
0 |
|a Field theory (Physics).
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| 690 |
|
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|a Electronic resources (E-books)
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| 700 |
1 |
|
|a Surowski, David.
|e author.
|4 aut
|4 http://id.loc.gov/vocabulary/relators/aut
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| 710 |
2 |
|
|a SpringerLink (Online service)
|
| 773 |
0 |
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|t Springer eBooks
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| 830 |
|
0 |
|a Springer eBook Collection.
|
| 856 |
4 |
0 |
|u https://holycross.idm.oclc.org/login?auth=cas&url=https://doi.org/10.1007/978-3-319-19734-0
|3 Click to view e-book
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