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



Source work progress
* : $\S 8$ -- revisiting from start, as follows:


 * : $\S 6$. Indexed families; partitions; equivalence relations: Exercise $8$