Book:T.S. Blyth/Set Theory and Abstract Algebra

Subject Matter

 * Set Theory
 * Abstract Algebra

Contents

 * Preface


 * 1: Set Theory and the Natural Numbers
 * $$\S 1$$. Sets; inclusion; intersection; union; complementation; number systems
 * $$\S 2$$. Sets of sets
 * $$\S 3$$. Ordered pairs; cartesian product sets
 * $$\S 4$$. Relations; functional relations; mappings
 * $$\S 5$$. Induced mappings; composition; injections; surjections; bijections
 * $$\S 6$$. Indexed families; partitions; equivalence relations
 * $$\S 7$$. Order relations; ordered sets; order isomorphisms; lattices
 * $$\S 8$$. Equipotent sets; cardinal arithmetic; $$\N$$
 * $$\S 9$$. Recursion; characterisation of $$\N$$
 * $$\S 10$$. Infinite cardinals


 * 2: Algebraic Structures and the Number System
 * $$\S 11$$. Laws of composition; semigroups; morphisms
 * $$\S 12$$. Groups; subgroups; group morphisms
 * $$\S 13$$. Embedding a cancellable abelian semigroup in a group; $$\Z$$
 * $$\S 14$$. Compatible equivalence relations on groups; quotient groups; isomorphism theorems; cyclic groups
 * $$\S 15$$. Rings; subrings; compatible equivalences on rings; ideals; ring morphisms
 * $$\S 16$$. Integral domains; division rings; fields
 * $$\S 17$$. Arithmetic properties in commutative integral domains; unique factorisation domains; principal ideal domains; euclidean domains
 * $$\S 18$$. Fields of quotients of a commutative integral domain; $$\Q$$; characteristic of a ring; ordered integral domains
 * $$\S 19$$. Archimedean, Cauchy complete and Dedekind complete ordered fields; $$\R$$
 * $$\S 20$$. Polynomials; $$\C$$


 * Index