Author(s): N. P. Chaudhuri
Publisher: Tata McGraw-Hill
Year: 1983
Language: English
City: New Delhi
Title
Preface
Contents
List of Symbols
1. Sets
1.1. Introduction
1.2. Mappings
1.3. Binary operations
1.4. Equivalence relations
1.5. Groupoids
1.6. Semigroups
1.7. Homomorphisms and isomorphisms
2. Groups
2.1. Groups
2.2. Subgroups
2.3. Cyclic groups
2.4. Isomorphisms
2.5. Group of permutations
2.6. Decomposition of a group
2.7. Normal subgroups and factor groups
2.8. Homomorphisms
2.9. Automorphisms
2.10. Groups with operators
3. Rings
3.1. Rings, subrings and integral domains
3.2. Division rings, fields
3.3. The characteristic of a ring
3.4. The field of quotients of an integral domain
3.5. Ideals
3.6. Factor rings
3.7. Homomorphisms
3.8. Principal ideals
3.9. Prime ideals and maximal ideals
3.10. Polynomial rings
3.11. Factorisation in F[x]
3.12. Euclidean rings
3.13. Unique factorisation domains
3.14. Irreducibility in Q[x]
4. Vector Spaces
4.1. Vector spaces
4.2. Linear independence
4.3. Bases and dimensions
4.4. Subspaces
4.5. Quotient spaces
4.6. Homomorphisms
5. Lattices
5.1. Order relations
5.2. Special elements which can exist in a poset
5.3. Lattices
5.4. Elementary properties
5.5. Complete lattices
5.6. Modular lattices
5.7. Metric lattices
5.8. Distributive lattices
5.9. Complemented lattices
5.10. Boolean algebras
6. Fields
6.1. Prime ideals
6.2. Extension fields
6.3. Splitting fields
6.4. Separability
6.5. Roots of unity
6.6. Galois fields
References
Answers to Selected Problems
Index
