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035   $a(OCoLC)1066187733
035   $a(PPN)226696839
035   $a(EXLCZ)994100000003359545
100   $a20180413d2018      u|         0
101 0 $aeng
135   $aurnn|008mamaa
181   $ctxt$2rdacontent
182   $cc$2rdamedia
183   $acr$2rdacarrier
200 10$aAbstract Algebra $eAn Introductory Course /$fby Gregory T. Lee
205   $a1st ed. 2018.
210  1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2018.
215   $a1 online resource (XI, 301 p. 7 illus.) 
225 1 $aSpringer Undergraduate Mathematics Series,$x1615-2085
300   $aIncludes index.
311   $a3-319-77648-7 
327   $aPart I Preliminaries -- 1 Relations and Functions -- 2 The Integers and Modular Arithmetic -- Part II Groups -- 3 Introduction to Groups -- 4 Factor Groups and Homomorphisms -- 5 Direct Products and the Classification of Finite Abelian Groups -- 6 Symmetric and Alternating Groups -- 7 The Sylow Theorems -- Part III Rings -- 8 Introduction to Rings -- 9 Ideals, Factor Rings and Homomorphisms -- 10 Special Types of Domains -- Part IV Fields and Polynomials -- 11 Irreducible Polynomials -- 12 Vector Spaces and Field Extensions -- Part V Applications -- 13 Public Key Cryptography -- 14 Straightedge and Compass Constructions -- A The Complex Numbers -- B Matrix Algebra -- Solutions -- Index.
330   $aThis carefully written textbook offers a thorough introduction to abstract algebra, covering the fundamentals of groups, rings and fields. The first two chapters present preliminary topics such as properties of the integers and equivalence relations. The author then explores the first major algebraic structure, the group, progressing as far as the Sylow theorems and the classification of finite abelian groups. An introduction to ring theory follows, leading to a discussion of fields and polynomials that includes sections on splitting fields and the construction of finite fields. The final part contains applications to public key cryptography as well as classical straightedge and compass constructions. Explaining key topics at a gentle pace, this book is aimed at undergraduate students. It assumes no prior knowledge of the subject and contains over 500 exercises, half of which have detailed solutions provided.
410  0$aSpringer Undergraduate Mathematics Series,$x1615-2085
606   $aGroup theory
606   $aAssociative rings
606   $aRings (Algebra)
606   $aAlgebra
606   $aField theory (Physics)
606   $aGroup Theory and Generalizations$3https://scigraph.springernature.com/ontologies/product-market-codes/M11078
606   $aAssociative Rings and Algebras$3https://scigraph.springernature.com/ontologies/product-market-codes/M11027
606   $aField Theory and Polynomials$3https://scigraph.springernature.com/ontologies/product-market-codes/M11051
615  0$aGroup theory.
615  0$aAssociative rings.
615  0$aRings (Algebra).
615  0$aAlgebra.
615  0$aField theory (Physics).
615 14$aGroup Theory and Generalizations.
615 24$aAssociative Rings and Algebras.
615 24$aField Theory and Polynomials.
676   $a512.02
700   $aLee$b Gregory T$4aut$4http://id.loc.gov/vocabulary/relators/aut$0474809
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910300108203321
996   $aAbstract Algebra$91563199
997   $aUNINA