02751nam a22004335i 4500001001800000003000900018005001700027007001500044008004100059020001800100024003100118050001400149072001600163072002300179082001200202100002600214245006700240250001900307264004600326300003400372336002600406337002600432338003600458347002400494490005100518505017600569520126500745650001702010650001302027650002802040650001702068650001302085650003402098710003402132773002002166776003602186830005102222856004402273978-0-387-27475-1DE-He21320180115171353.0cr nn 008mamaa100301s2005 xxu| s |||| 0|eng d a97803872747517 a10.1007/0-387-27475-82doi 4aQA150-272 7aPBF2bicssc 7aMAT0020002bisacsh04a5122231 aLang, Serge.eauthor.10aUndergraduate Algebrah[electronic resource] /cby Serge Lang. aThird Edition. 1aNew York, NY :bSpringer New York,c2005. aXII, 389 p.bonline resource. atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda1 aUndergraduate Texts in Mathematics,x0172-60560 aThe Integers -- Groups -- Rings -- Polynomials -- Vector Spaces and Modules -- Some Linear Groups -- Field Theory -- Finite Fields -- The Real and Complex Numbers -- Sets. aUndergraduate 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 Snyderâ€™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. 0aMathematics. 0aAlgebra. 0aField theory (Physics).14aMathematics.24aAlgebra.24aField Theory and Polynomials.2 aSpringerLink (Online service)0 tSpringer eBooks08iPrinted edition:z9780387220253 0aUndergraduate Texts in Mathematics,x0172-605640uhttp://dx.doi.org/10.1007/0-387-27475-8