## ＜電子ブック＞Abstract Algebra : An Introductory Course

責任表示 by Gregory T. Lee Lee, Gregory T SpringerLink (Online service) English (英語) Springer International Publishing Imprint: Springer 2018- Cham, Germany シリーズ Springer Undergraduate Mathematics Series 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 pro...perties 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.続きを見る Part I Preliminaries1 Relations and Functions2 The Integers and Modular ArithmeticPart II Groups3 Introduction to Groups4 Factor Groups and Homomorphisms5 Direct Products and the Classification of Finite Abelian Groups6 Symmetric and Alternating Groups7 The Sylow TheoremsPart III Rings8 Introduction to Rings9 Ideals, Factor Rings and Homomorphisms10 Special Types of DomainsPart IV Fields and Polynomials11 Irreducible Polynomials12 Vector Spaces and Field ExtensionsPart V Applications13 Public Key Cryptography14 Straightedge and Compass ConstructionsA The Complex NumbersB Matrix AlgebraSolutionsIndex.続きを見る http://hdl.handle.net/2324/1001657206 Full text available from SpringerLINK ebooks - Mathematics and Statistics (2018)

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レコードID 1932065 QA174-183 512.2 Mathematics. Associative rings. Rings (Algebra). Algebra. Field theory (Physics). Group theory. Mathematics. Group Theory and Generalizations. Associative Rings and Algebras. Field Theory and Polynomials. ssj0002000336 9783319776484[3319776487](print) 9783319776491[3319776495] 2018.06.06 2018.06.06