1: (A) Write True (T) in front of the true statement and false (F) in front the false atement: 1. Every subset of a ring R is also a ring. 2. The elements 1 and 3 are nilpotent in the ring (Z9, +9,9). 3. (R, +,.) is a Boolean ring. 4. (Z, +..) is a field. 5. Any ring must be commutative. 6. Every ring is a group. 7. In (Z5, +5,-5), the only zero divisor element is 0.
1: (A) Write True (T) in front of the true statement and false (F) in front the false atement: 1. Every subset of a ring R is also a ring. 2. The elements 1 and 3 are nilpotent in the ring (Z9, +9,9). 3. (R, +,.) is a Boolean ring. 4. (Z, +..) is a field. 5. Any ring must be commutative. 6. Every ring is a group. 7. In (Z5, +5,-5), the only zero divisor element is 0.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![Q1: (A) Write True (T) in front of the true statement and false (F) in front the false
statement:
1. Every subset of a ring R is also a ring.
2. The elements 1 and 3 are nilpotent in the ring (Z9, +9,9).
3. (R, +,.) is a Boolean ring.
4. (Z, +,.) is a field.
5. Any ring must be commutative.
6. Every ring is a group.
7. In (Z5, +5,-5), the only zero divisor element is 0.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6cbdddb7-a1d2-4b9d-ac61-e29abe78dea2%2Ff9de2389-5522-462e-b08b-0b6e5926a25e%2F0nmx6_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Q1: (A) Write True (T) in front of the true statement and false (F) in front the false
statement:
1. Every subset of a ring R is also a ring.
2. The elements 1 and 3 are nilpotent in the ring (Z9, +9,9).
3. (R, +,.) is a Boolean ring.
4. (Z, +,.) is a field.
5. Any ring must be commutative.
6. Every ring is a group.
7. In (Z5, +5,-5), the only zero divisor element is 0.
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