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Solutions for Modern Algebra: An Introduction | 6th Edition | ISBN: 9780470384435 | Authors: John R. Durbin 9780470384435

Solution for problem 16.8 Chapter 16

Consider Z as a subgroup of lR with addition as the operation. Think of the elements of

Modern Algebra: An Introduction | 6th Edition


Problem 16.8

Consider Z as a subgroup of lR with addition as the operation. Think of the elements of lRas the points on a directed line in the usual way, and then describe the right cosets of Z in lRgeometrically. (Suggestion: Start with a specific example, such as Z + ~.)

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Step-by-Step Solution:

Step 1 of 2

Consider Z as a subgroup ofwith addition as the operation

So, be the group under addition

So, it is geometrically viewed as the horizontal axis

If it is considered to be the group under multiplication, then the entire xy-plane is its picture

is the subgroup of

Chapter 16, Problem 16.8 is Solved

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Consider Z as a subgroup of lR with addition as the operation. Think of the elements of