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.

Abstract and Geometric Algebra Mathematics

Tác giả: Michael Janssen & Melissa Lindsey
Nhà xuất bản: Dordt University & University of Wisconsin-Madison
Nguồn: LibreTexts
Giấy phép: CC BY-SA
Ngôn ngữ: EN
Danh mục: Khoa học cơ bản

Đọc trực tuyến Tải PDF (nguồn mở)

Mục lục· 18 mục

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