Author(s): Seth Warner
Series: PRENTICE-HALL MATHEMATICS SERIES
Edition: 1
Publisher: Prentice Hall
Year: 1965
Language: English
Commentary: Original Version in 1965
Pages: 457
City: Englewood Cliffs
Chapter I. ALGEBRAIC STRUCTURES 1
1. The Language of Set Theory 2
2. Compositions 10
3. Unions and Intersections of Sets 17
4. Neutral Elements and Inverses 23
5. Composites and Inverses of Functions 29
6. Isomorphisms of Algebraic Structures 36
7. Semigroups and Groups 46
Chapter II. NEW STRUCTURES FROM OLD 52
8. Compositions Induced on Subsets 52
9. Compositions Induced on the Set of All Subsets 61
10. Equivalence Relations 64
11. Quotient Structures 70
12. Homomorphisms 81
13. Compositions Induced on Cartesian Products and Function Spaces 90
Chapter III. THE NATURAL NUMBERS 100
14. Orderings 100
15. Ordered Semigroups 113
16. The Natural Numbers 117
17. Finite Sets 137
18. Induced N-ary Operations 143
19. Combinatorial Analysis 162
Chapter IV. RINGS AND FIELDS 168
20. The Integers 168
21. Rings and Integral Domains 188
22. New Rings from Old 198
23. The Field of Rational Numbers 210
24. The Division Algorithm 225
25. Cyclic Groups and Lagrange’s Theorem 236
Chapter V. VECTOR SPACES
26. Vector Spaces and Modules 251
27. Subspaces and Bases 258
28. Linear Transformations 274
29. Matrices 290
30. Linear Equations 305
31. Direct Sums and Quotient Spaces 322
32. Rings of Linear Operators 340
Chapter VI. POLYNOMIALS
33. Algebras 356
34. The Algebra of Polynomials 367
35. Principal Ideal Domains 377
36. Substitution 395
37. Irreducibility Criteria 407
38. Adjoining Roots 416
39. Finite Fields and Division Rings 428
40. Polynomials in Several Indeterminates 443
LIST OF SYMBOLS i
INDEX iii
