UID:
almahu_9949697579302882
Format:
1 online resource (251 p.)
ISBN:
1-281-76329-2
,
9786611763299
,
0-08-087315-4
Series Statement:
Pure and Applied Mathematics : A Series of Monographs and Textbooks ; 7
Content:
Fundamental concepts of algebra
Note:
Includes index.
,
Front Cover; Fundamental Concepts of Algebra; Copyright Page; Contents; Preface; Prerequisite knowledge and terminological conventions; Chapter I. Monoids; 1. Definition of a monoid; 2. Submonoids. Generators; 3. Homomorphisms; 4. Quotient monoids; 5. Products; 6. Free monoids; Exercises; Chapter II. Groups; 1. Definition of a group; 2. Subgroups; 3. Homomorphisms. Quotient groups; 4. Groups operating on a set; 5.Products of groups; 6. Free groups; Exercises; Chapter III. Rings and modules; 1. Rings; 2. Field of quotients; 3. Modules; 4. Submodules; 5. Linear mappings; 6. Products
,
7. Uniqueness theorems for semi-simple modules8. Tensor products of modules; 9. Free modules. Bases; 10. Multilinear mappings; 11. Transfer of basic rings; 12. Vector spaces; 13. Vector spaces in duality; 14. The rank of a linear mapping; 15. Matrices; 16. Systems of linear equations; 17. Graded modules; Exercises; Chapter IV. Algebras; 1. Definition; 2. Subalgebras; 3. Homomorphisms; 4. Products; 5. Free algebra; Exercises; Chapter V. Associative algebras; 1. Definitions; 2. Graded algebras; 3. Tensor algebras; 4. Tensor products of graded algebras; 5. Anticommutative algebras
,
6. Derivations7. Exterior algebras; 8. Grassmann algebras; 9. The determinant of a matrix; 10. Some applications of determinants; 11. Existence of certain derivations; 12. The trace of a matrix; 13. Alternating multilinear mappings; 14. The Pfaffian of an alternating bilinear form; 15. Exterior algebras on vector spaces; 16. Transfer of the basic ring; 17. Commutative tensor products; 18. Symmetric algebras; 19. Polynomial algebras; Exercises; Index
,
English
Additional Edition:
ISBN 0-12-172050-0
Language:
English
