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Synopsis
This book is designed as a text for a first-year graduate algebra course. The choice of topics is guided by the underlying theme of modules as a basic unifying concept in mathematics. Beginning with standard topics in groups and ring theory, the authors then develop basic module theory, culminating in the fundamental structure theorem for finitely generated modules over a principal ideal domain. They then treat canonical form theory in linear algebra as an application of this fundamental theorem. Module theory is also used in investigating bilinear, sesquilinear, and quadratic forms. The authors develop some multilinear algebra (Hom and tensor product) and the theory of semisimple rings and modules and apply these results in the final chapter to study group representations by viewing a representation of a group G over a field F as an F(G)-module. The book emphasizes proofs with a maximum of insight and a minimum of computation in order to promote understanding. However, extensive material on computation (for example, computation of canonical forms) is provided.
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- PublisherSpringer
- Publication date1992
- ISBN 10 0387978399
- ISBN 13 9780387978390
- BindingHardcover
- LanguageEnglish
- Number of pages536
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Algebra: An Approach via Module Theory
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Hardcover. Condition: ex library-good. Graduate Texts in Mathematics 136. x, 526 p. 24 cm. Ex library with labels on spine and inside rear cover, ink stamps on top edge and series page. Spine faded, marks on rear cover. Seller Inventory # 148886
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Hardcover. Condition: Very Good. 1992. Corr. 2nd Printing 1999 ed. New York, NY: Springer, 1999. 1992. Corr. 2nd Printing 1999 ed. Very Good. New York, NY: Springer, 1999. 1992. Corr. 2nd Printing 1999 ed. Hard cover. 4. null Sewn binding. Cloth over boards. 526 p. Graduate Texts in Mathematics, 136. Audience: General/trade. ORIGINAL hardcover; ex library (Germany); has some shelf wear; otherwise a tight bright unmarked copy in very good shape overall; appears unread. Seller Inventory # 74929
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Hardcover. Condition: New. 1992. Corr. 2nd Printing 1999 ed. New York, NY: Springer, 1999. 1992. Corr. 2nd Printing 1999 ed. New. New York, NY: Springer, 1999. 1992. Corr. 2nd Printing 1999 ed. Hard cover. 6. null Sewn binding. Cloth over boards. 526 p. Graduate Texts in Mathematics, 136. Audience: General/trade. BRAND NEW hardcover reprint [as issued by the publisher]; never read! Seller Inventory # 74428
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Algebra: An Approach via Module Theory
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New York : Springer-Verlag, 1992
ISBN 10: 0387978399
ISBN 13: 9780387978390
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