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" Algebra : "
Ernest Shult, David Surowski
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BL
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| Record Number
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649926
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dltt
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| Main Entry
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Shult, Ernest
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| Title & Author
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Algebra : : a teaching and source book /\ Ernest Shult, David Surowski
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| Page. NO
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1 online resource (xxii, 539 pages) :: illustrations
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| ISBN
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9783319197340
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: 3319197347
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9783319197333
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| Bibliographies/Indexes
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Includes bibliographical references and index
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| Contents
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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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| Abstract
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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 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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| Subject
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Algebra.
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Group Theory and Generalizations.
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Field Theory and Polynomials.
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Algebra.
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| Dewey Classification
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512
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| LC Classification
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QA152.3
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| Added Entry
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Surowski, David,1949-
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Ohio Library and Information Network.
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