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Abstract Algebra : An Introductory Course / / by Gregory T. Lee



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Autore: Lee Gregory T Visualizza persona
Titolo: Abstract Algebra : An Introductory Course / / by Gregory T. Lee Visualizza cluster
Pubblicazione: Cham : , : Springer International Publishing : , : Imprint : Springer, , 2018
Edizione: 1st ed. 2018.
Descrizione fisica: 1 online resource (XI, 301 p. 7 illus.)
Disciplina: 512.02
Soggetto topico: Group theory
Associative rings
Rings (Algebra)
Algebra
Field theory (Physics)
Group Theory and Generalizations
Associative Rings and Algebras
Field Theory and Polynomials
Note generali: Includes index.
Nota di contenuto: Part 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.
Sommario/riassunto: This 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.
Titolo autorizzato: Abstract Algebra  Visualizza cluster
ISBN: 3-319-77649-5
Formato: Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione: Inglese
Record Nr.: 9910300108203321
Lo trovi qui: Univ. Federico II
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Serie: Springer Undergraduate Mathematics Series, . 1615-2085