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Chapter 2 Ring Fundamentals

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Book Id: WPLBN0000673787
Format Type: PDF eBook
File Size: 221.96 KB
Reproduction Date: 2005

Title: Chapter 2 Ring Fundamentals  
Language: English
Subject: Science., Mathematics, Logic
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Chapter 2 Ring Fundamentals. (n.d.). Chapter 2 Ring Fundamentals. Retrieved from

Mathematics document containing theorems and formulas.

Excerpt: Basic Definitions and Properties. Definitions and Comments A ring R is an abelian group with a multiplication operation (a, b) - ab that is associative and satisfies the distributive laws: a(b+c) = ab+ac and (a + b)c = ab + ac for all a, b, c E R. We will always assume that R has at least two elements, including a multiplicative identity 1R satisfying a1R = 1Ra = a for all a in R. The multiplicative identity is often written simply as 1, and the additive identity as 0. If a, b, and c are arbitrary elements of R, the following properties are derived quickly from the definition of a ring; we sketch the technique in each case.


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