Book:T.S. Blyth/Set Theory and Abstract Algebra
Jump to navigation
Jump to search
T.S. Blyth: Set Theory and Abstract Algebra
Published $\text {1975}$, Longman Mathematical Texts
- ISBN 0 582 44284 2
Subject Matter
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
- 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 $8$