Abstract Algebra An Introductory Course /

• Κύριος συγγραφέας: Lee, Gregory T. (Συγγραφέας, http://id.loc.gov/vocabulary/relators/aut)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Cham : Springer International Publishing : Imprint: Springer, 2018.
• Έκδοση: 1st ed. 2018.
• Σειρά: Springer Undergraduate Mathematics Series,
• Θέματα: Group theory.; Associative rings.; Rings (Algebra).; Algebra.; Field theory (Physics).; Group Theory and Generalizations.; Associative Rings and Algebras.; Field Theory and Polynomials.

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 algebrai...

Πίνακας περιεχομένων:

• 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.