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

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T.S. Blyth: Set Theory and Abstract Algebra

Published $1975$, Longman Mathematical Texts

ISBN 0 582 44284 2.

Subject Matter


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; $\C$