{"product_id":"first-course-in-abstract-algebra-a-9781292024967","title":"First Course in Abstract Algebra A","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e Considered a classic by many, \u003cstrong\u003e\u003cem\u003eA First Course in Abstract Algebra\u003c\/em\u003e\u003c\/strong\u003e is an in-depth introduction to abstract algebra. Focused on groups, rings and fields, this text gives students a firm foundation for more specialised work by emphasising an understanding of the nature of algebraic structures.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cul\u003e\n\u003cli\u003e0. Sets and Relations. \u003c\/li\u003e\n\u003cli\u003eI. GROUPS AND SUBGROUPS. \u003c\/li\u003e\n\u003cli\u003e1. Introduction and Examples. \u003c\/li\u003e\n\u003cli\u003e2. Binary Operations. \u003c\/li\u003e\n\u003cli\u003e3. Isomorphic Binary Structures. \u003c\/li\u003e\n\u003cli\u003e4. Groups. \u003c\/li\u003e\n\u003cli\u003e5. Subgroups. \u003c\/li\u003e\n\u003cli\u003e6. Cyclic Groups. \u003c\/li\u003e\n\u003cli\u003e7. Generators and Cayley Digraphs. \u003c\/li\u003e\n\u003cli\u003eI. PERMUTATIONS, COSETS, AND DIRECT PRODUCTS. \u003c\/li\u003e\n\u003cli\u003e8. Groups of Permutations. \u003c\/li\u003e\n\u003cli\u003e9. Orbits, Cycles, and the Alternating Groups. \u003c\/li\u003e\n\u003cli\u003e10. Cosets and the Theorem of Lagrange. \u003c\/li\u003e\n\u003cli\u003e11. Direct Products and Finitely Generated Abelian Groups. \u003c\/li\u003e\n\u003cli\u003e12. Plane Isometries. \u003c\/li\u003e\n\u003cli\u003eIII. HOMOMORPHISMS AND FACTOR GROUPS. \u003c\/li\u003e\n\u003cli\u003e13. Homomorphisms. \u003c\/li\u003e\n\u003cli\u003e14. Factor Groups. \u003c\/li\u003e\n\u003cli\u003e15. Factor-Group Computations and Simple Groups. \u003c\/li\u003e\n\u003cli\u003e16. Group Action on a Set. \u003c\/li\u003e\n\u003cli\u003e17. Applications of G-Sets to Counting. \u003c\/li\u003e\n\u003cli\u003eIV. RINGS AND FIELDS. \u003c\/li\u003e\n\u003cli\u003e18. Rings and Fields. \u003c\/li\u003e\n\u003cli\u003e19. Integral Domains. \u003c\/li\u003e\n\u003cli\u003e20. Fermat's and Euler's Theorems. \u003c\/li\u003e\n\u003cli\u003e21. The Field of Quotients of an Integral Domain. \u003c\/li\u003e\n\u003cli\u003e22. Rings of Polynomials. \u003c\/li\u003e\n\u003cli\u003e23. Factorization of Polynomials over a Field. \u003c\/li\u003e\n\u003cli\u003e24. Noncommutative Examples. \u003c\/li\u003e\n\u003cli\u003e25. Ordered Rings and Fields. \u003c\/li\u003e\n\u003cli\u003eV. IDEALS AND FACTOR RINGS. \u003c\/li\u003e\n\u003cli\u003e26. Homomorphisms and Factor Rings. \u003c\/li\u003e\n\u003cli\u003e27. Prime and Maximal Ideas. \u003c\/li\u003e\n\u003cli\u003e28. Gröbner Bases for Ideals. \u003c\/li\u003e\n\u003cli\u003eVI. EXTENSION FIELDS. \u003c\/li\u003e\n\u003cli\u003e29. Introduction to Extension Fields. \u003c\/li\u003e\n\u003cli\u003e30. Vector Spaces. \u003c\/li\u003e\n\u003cli\u003e31. Algebraic Extensions. \u003c\/li\u003e\n\u003cli\u003e32. Geometric Constructions. \u003c\/li\u003e\n\u003cli\u003e33. Finite Fields. \u003c\/li\u003e\n\u003cli\u003eVII. ADVANCED GROUP THEORY. \u003c\/li\u003e\n\u003cli\u003e34. Isomorphism Theorems. \u003c\/li\u003e\n\u003cli\u003e35. Series of Groups. \u003c\/li\u003e\n\u003cli\u003e36. Sylow Theorems. \u003c\/li\u003e\n\u003cli\u003e37. Applications of the Sylow Theory. \u003c\/li\u003e\n\u003cli\u003e38. Free Abelian Groups. \u003c\/li\u003e\n\u003cli\u003e39. Free Groups. \u003c\/li\u003e\n\u003cli\u003e40. Group Presentations. \u003c\/li\u003e\n\u003cli\u003eVIII.. AUTOMORPHISMS AND GALOIS THEORY. \u003c\/li\u003e\n\u003cli\u003e41. Automorphisms of Fields. \u003c\/li\u003e\n\u003cli\u003e42. The Isomorphism Extension Theorem. \u003c\/li\u003e\n\u003cli\u003e43. Splitting Fields. \u003c\/li\u003e\n\u003cli\u003e44. Separable Extensions. \u003c\/li\u003e\n\u003cli\u003e45. Totally Inseparable Extensions. \u003c\/li\u003e\n\u003cli\u003e46. Galois Theory. \u003c\/li\u003e\n\u003cli\u003e47. Illustrations of Galois Theory. \u003c\/li\u003e\n\u003cli\u003e48. Cyclotomic Extensions. \u003c\/li\u003e\n\u003cli\u003e49. Insolvability of the Quintic. \u003c\/li\u003e\n\u003cli\u003eAppendix: Matrix Algebra. \u003c\/li\u003e\n\u003cli\u003eNotations.  \u003c\/li\u003e\n\u003cli\u003eIndex. \u003c\/li\u003e\n\u003c\/ul\u003e","brand":"Pearson Education","offers":[{"title":"Default Title","offer_id":51019578048855,"sku":"9781292024967","price":64.59,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781292024967.jpg?v=1750780683","url":"https:\/\/bookcurl.com\/products\/first-course-in-abstract-algebra-a-9781292024967","provider":"Book Curl","version":"1.0","type":"link"}