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Rings with Inquiry
One of the concepts fundamental to the historical development of algebra is the notion of factorization; closely related questions that have driven the development of algebra over the centuries are: when does a polynomial equation have solutions in a particular number system, and is there a systematic way to find them? The goal of this book is to explore the idea of factorization from an abstract perspective.
- Author
- Michael Janssen & Melissa Lindsey
- Publisher
- Dordt University & University of Wisconsin-Madison
- Source
- LibreTexts
- License
- CC BY-SA
- Language
- EN
- Category
- Basic Sciences
Contents· 18 sections
- 01: The Integers
- 1.01: Induction and Well-Ordering
- 1.02: Divisibility and GCDs in the Integers
- 1.03: Primes and Factorization
- 1.04: The Integers modulo m
- 02: Fields and Rings
- 2.01: Fields
- 2.02: Rings
- 2.03: Divisibility in Integral Domains
- 2.04: Principal Ideals and Euclidean Domains
- 03: Factorization
- 3.01: Factoring Polynomials
- 3.02: Factorization in Euclidean Domains
- 3.03: Nonunique Factorization
- 04: Ideals and Homomorphisms and test
- 4.01: Ideals in general
- 4.02: Homomorphisms
- 4.03: Quotient Rings: New Rings from Old