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Let m and n be positive integers and let k be the least

Contemporary Abstract Algebra | 8th Edition | ISBN: 9781133599708 | Authors: Joseph Gallian ISBN: 9781133599708 52

Solution for problem 36E Chapter 12

Contemporary Abstract Algebra | 8th Edition

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Contemporary Abstract Algebra | 8th Edition | ISBN: 9781133599708 | Authors: Joseph Gallian

Contemporary Abstract Algebra | 8th Edition

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Problem 36E

Problem 36E

Let m and n be positive integers and let k be the least common multiple of m and n. Show that mZ nZ = kZ.

Step-by-Step Solution:

36. Let m and n be positive integers and let k be the least common multiple of m and n. Show that .

Step By Step Solution

Step 1 of 2

Given k is the least common multiple of m and n.

Also we know any set of the form  is ideal, so  and  are ideals.

( the set of integers. If  is any integer, we write  for the set .)

Step 2 of 2

Chapter 12, Problem 36E is Solved
Textbook: Contemporary Abstract Algebra
Edition: 8
Author: Joseph Gallian
ISBN: 9781133599708

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Let m and n be positive integers and let k be the least