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＜E-Book＞
Undergraduate Algebra / by Serge Lang
(Undergraduate Texts in Mathematics. ISSN:21975604)

Edition	3rd ed. 2005.
Publisher	(New York, NY : Springer New York : Imprint: Springer)
Year	2005
Language	English
Size	XII, 389 p : online resource
Authors	*Lang, Serge author SpringerLink (Online service)
Subjects	LCSH:Algebra LCSH:Algebraic fields LCSH:Polynomials FREE:Algebra FREE:Field Theory and Polynomials
Notes	The Integers -- Groups -- Rings -- Polynomials -- Vector Spaces and Modules -- Some Linear Groups -- Field Theory -- Finite Fields -- The Real and Complex Numbers -- Sets Undergraduate Algebra is a text for the standard undergraduate algebra course. It concentrates on the basic structures and results of algebra, discussing groups, rings, modules, fields, polynomials, finite fields, Galois Theory, and other topics. The author has also included a chapter on groups of matrices which is unique in a book at this level. Throughout the book, the author strikes a balance between abstraction and concrete results, which enhance each other. Illustrative examples accompany the general theory. Numerous exercises range from the computational to the theoretical, complementing results from the main text. For the third edition, the author has included new material on product structure for matrices (e.g. the Iwasawa and polar decompositions), as well as a description of the conjugation representation of the diagonal group. He has also added material on polynomials, culminating in Noah Snyder’s proof of the Mason-Stothers polynomial abc theorem. About the First Edition: The exposition is down-to-earth and at the same time very smooth. The book can be covered easily in a one-year course and can be also used in a one-term course...the flavor of modern mathematics is sprinkled here and there. - Hideyuki Matsumura, Zentralblatt HTTP:URL=https://doi.org/10.1007/0-387-27475-8

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