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

T.S. Blyth: Set Theory and Abstract Algebra

Published $\text {1975}$, Longman Mathematical Texts

ISBN 0 582 44284 2

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

Next

Source work progress

• 1975: T.S. Blyth: Set Theory and Abstract Algebra ... (previous) ... (next): $\S 8$ -- revisiting from start, as follows:

• 1975: T.S. Blyth: Set Theory and Abstract Algebra ... (previous) ... (next): $\S 6$. Indexed families; partitions; equivalence relations: Exercise $8$