Holy Name University Library

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Abstract algebra / Dan Saracino.

By: Saracino, Dan.
London, United Kingdom : Published by ED-Tech Press, ©2022Edition: Second, Global edition.Description: 313 pages ; 23 cm.ISBN: 9781804060032 .Subject(s): Abstract algebraDDC classification: 512.02 Sa71
Contents:
1. Binary Operations 2. Groups 3. Fundamental Theorems about Groups 4. Powers of an Element; Cyclic Groups 5. Subgroups 6. Direct Products 7. Functions 8. Symmetric Groups 9. Equivalence Relations; Cosets 10. Counting the Elements of a Finite Group 11. Normal Groups 12. Homomorphisms 13. Homomorphisms and Normal Subgroups 14. Direct Products and Finite Abelian Groups 15. Sylow Theorems 16. Rings 17. Subrings, Ideals, and Quotient Rings 18. Ring Homomorphisms 19. Polynomials 20. From Polynomials to Fields 21. Unique Factorization Domains 22. Extension of Fields 23. Constructions with Straightedge and Compass 24. Normal and Separable Extensions 25. Galois Theory 26. Solvability
Summary: The presentation of the sections is given at a higher level. Unusual features, for a book is still relatively short, are the inclusion of full proofs of both directions of Gauss' theorem on constructible regular polygons and Galois' theorem on solvability by radicals, a Galois-theoretic proof of the Fundamental Theorem of Algebra, and proof of the Primitive Element of Theorem.
Item type Current location Collection Call number Status Date due Barcode
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General Circulation Section 		GC GC 512.02 Sa71 2022 (Browse shelf) Available HNU004344
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GC 512 C54 2019 Intermediate algebra : GC 512.02 M91 2017 Abstract algebra : GC 512.02 M91 2017 Abstract algebra : GC 512.02 Sa71 2022 Abstract algebra / GC 512.076 L32 2022 Algebra & trig with CalcChat and CalcView / GC 512.076 St45 2022 Algebra 1 : GC 512.1 H71 A primer for calculus /

Includes index.

1. Binary Operations
2. Groups
3. Fundamental Theorems about Groups
4. Powers of an Element; Cyclic Groups
5. Subgroups
6. Direct Products
7. Functions
8. Symmetric Groups
9. Equivalence Relations; Cosets
10. Counting the Elements of a Finite Group
11. Normal Groups
12. Homomorphisms
13. Homomorphisms and Normal Subgroups
14. Direct Products and Finite Abelian Groups
15. Sylow Theorems
16. Rings
17. Subrings, Ideals, and Quotient Rings
18. Ring Homomorphisms
19. Polynomials
20. From Polynomials to Fields
21. Unique Factorization Domains
22. Extension of Fields
23. Constructions with Straightedge and Compass
24. Normal and Separable Extensions
25. Galois Theory
26. Solvability

The presentation of the sections is given at a higher level. Unusual features, for a book is still relatively short, are the inclusion of full proofs of both directions of Gauss' theorem on constructible regular polygons and Galois' theorem on solvability by radicals, a Galois-theoretic proof of the Fundamental Theorem of Algebra, and proof of the Primitive Element of Theorem.

College of Education Bachelor of Secondary Education major in Mathematics

in English

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