Introduction to abstract algebra / Jonathan D.H. Smith, Iowa State University, Ames, Iowa, USA

Author:: Smith, Jonathan D. H., 1949-
Published:: Boca Raton : CRC Press, Taylor & Francis Group, [2016]
Edition:: Second edition.
Physical Description:: xii, 340 pages : illustrations ; 25 cm.

Availability

Finding items...

Series:

Textbooks in mathematics

Contents:

Machine generated contents note: 1.1.Ordering numbers -- 1.2.The Well-Ordering Principle -- 1.3.Divisibility -- 1.4.The Division Algorithm -- 1.5.Greatest common divisors -- 1.6.The Euclidean Algorithm -- 1.7.Primes and irreducibles -- 1.8.The Fundamental Theorem of Arithmetic -- 1.9.Exercises -- 1.10.Study projects -- 1.11.Notes -- 2.1.Specifying functions -- 2.2.Composite functions -- 2.3.Linear functions -- 2.4.Semigroups of functions -- 2.5.Injectivity and surjectivity -- 2.6.Isomorphisms -- 2.7.Groups of permutations -- 2.8.Exercises -- 2.9.Study projects -- 2.10.Notes -- 2.11.Summary -- 3.1.Kernel and equivalence relations -- 3.2.Equivalence classes -- 3.3.Rational numbers -- 3.4.The First Isomorphism Theorem for Sets -- 3.5.Modular arithmetic -- 3.6.Exercises -- 3.7.Study projects -- 3.8.Notes -- 4.1.Semigroups -- 4.2.Monoids -- 4.3.Groups -- 4.4.Componentwise structure -- 4.5.Powers -- 4.6.Submonoids and subgroups -- 4.7.Cosets -- 4.8.Multiplication tables -- 4.9.Exercises -- 4.10.Study projects -- 4.11.Notes -- 5.1.Homomorphisms -- 5.2.Normal subgroups -- 5.3.Quotients -- 5.4.The First Isomorphism Theorem for Groups -- 5.5.The Law of Exponents -- 5.6.Cayley's Theorem -- 5.7.Exercises -- 5.8.Study projects -- 5.9.Notes -- 6.1.Rings -- 6.2.Distributivity -- 6.3.Subrings -- 6.4.Ring homomorphisms -- 6.5.Ideals -- 6.6.Quotient rings -- 6.7.Polynomial rings -- 6.8.Substitution -- 6.9.Exercises -- 6.10.Study projects -- 6.11.Notes -- 7.1.Integral domains -- 7.2.Degrees -- 7.3.Fields -- 7.4.Polynomials over fields -- 7.5.Principal ideal domains -- 7.6.Irreducible polynomials -- 7.7.Lagrange interpolation -- 7.8.Fields of fractions -- 7.9.Exercises -- 7.10.Study projects -- 7.11.Notes -- 8.1.Factorization in integral domains -- 8.2.Noetherian domains -- 8.3.Unique factorization domains -- 8.4.Roots of polynomials -- 8.5.Splitting fields -- 8.6.Uniqueness of splitting fields -- 8.7.Structure of finite fields -- 8.8.Galois fields -- 8.9.Exercises -- 8.10.Study projects -- 8.11.Notes -- 9.1.Endomorphisms -- 9.2.Representing a ring -- 9.3.Modules -- 9.4.Submodules -- 9.5.Direct sums -- 9.6.Free modules -- 9.7.Vector spaces -- 9.8.Abelian groups -- 9.9.Exercises -- 9.10.Study projects -- 9.11.Notes -- 10.1.Actions -- 10.2.Orbits -- 10.3.Transitive actions -- 10.4.Fixed points -- 10.5.Faithful actions -- 10.6.Cores -- 10.7.Alternating groups -- 10.8.Sylow Theorems -- 10.9.Exercises -- 10.10.Study projects -- 10.11.Notes -- 11.1.Quasigroups -- 11.2.Latin squares -- 11.3.Division -- 11.4.Quasigroup homomorphisms -- 11.5.Quasigroup homotopies -- 11.6.Principal isotopy -- 11.7.Loops -- 11.8.Exercises -- 11.9.Study projects -- 11.10.Notes.

Subject(s):

Algebra, Abstract

ISBN:

9781498731614 (hardback ; acid-free paper)
1498731619 (hardback ; acid-free paper)

Note:

"A Chapman & Hall book."
Includes index.

View MARC record | catkey: 16612541