Q4: (A) Prove or disprove each of the following 1. Every prime ideal is maximal. 3. The cancellation law for multiplication holds in any ring. 2. Every subring is ideal.
Q4: (A) Prove or disprove each of the following 1. Every prime ideal is maximal. 3. The cancellation law for multiplication holds in any ring. 2. Every subring is ideal.
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter6: More On Rings
Section6.4: Maximal Ideals (optional)
Problem 14E
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![Q4: (A) Prove or disprove each of the following
1. Every prime ideal is maximal.
3. The cancellation law for multiplication holds in any ring.
2. Every subring is ideal.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1399653f-9f2d-4cb3-b867-20d5a3449fee%2F585b000a-01ef-49f5-9257-4e7943f9f13f%2Fgnpyor_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Q4: (A) Prove or disprove each of the following
1. Every prime ideal is maximal.
3. The cancellation law for multiplication holds in any ring.
2. Every subring is ideal.
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