Find Book on Intro Abstract Algebra: Rings, Fields, Polynomials

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SUMMARY

The discussion centers on finding a suitable introductory textbook for abstract algebra, specifically covering topics such as commutative rings, fields, polynomial rings, and key theorems like Fermat's and Euler's. A recommended resource is "Abstract Algebra" by Herstein, which aligns well with the course outline that includes concepts like the division algorithm, unique factorization, and finite fields. The forum also points to a dedicated textbook thread that may provide additional resources for learners.

PREREQUISITES
  • Understanding of basic algebraic structures such as rings and fields.
  • Familiarity with polynomial functions and their properties.
  • Knowledge of number theory concepts including primes and congruences.
  • Basic proof techniques including induction and equivalence relations.
NEXT STEPS
  • Research "Abstract Algebra" by Herstein for foundational concepts.
  • Explore the division algorithm and its applications in number theory.
  • Study the Chinese Remainder Theorem and its significance in modular arithmetic.
  • Investigate finite fields and their applications in coding theory.
USEFUL FOR

Students and educators in mathematics, particularly those focusing on abstract algebra, as well as anyone seeking to deepen their understanding of algebraic structures and their applications.

devious_
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I've been away for quite a while, and now I can't find the book forum. :confused:

Anyway, I'm looking for a book that covers introductory abstract algebra. The course outline is:
- (commutative) rings, fields, Z, Q, R, C, Z, polynomial rings, properties of Z.
- division algorithm, Euclidean algorithm, primes, congruences, Fermat & Euler theorems, unique factorization, linear and other congruence equations, Chinese Remainder Theorem
- sets, well-ordering, functions, equivalence relations, proof by induction, cardinality, existence of transcendentals
- finite fields, fundamental theorem of algebra, complex numbers
- polynomial rings, rational roots, irreducible polynomials, unique factorization

Thank you.
 
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