Q2: (A) Choose the correct answer for each of the following: 1. The cancellation law holds in a. any ring b. a commutative ring 2. The ring of even numbers (Ze, +, .) is c. an integral domain ring
Q2: (A) Choose the correct answer for each of the following: 1. The cancellation law holds in a. any ring b. a commutative ring 2. The ring of even numbers (Ze, +, .) is c. an integral domain ring
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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Question
![Q2: (A) Choose the correct answer for each of the following:
1. The cancellation law holds in
a. any ring
b. a commutative ring
2. The ring of even numbers (Ze, +, .) is.
a. with identity
b. with zero divisor
3. The elements 2 and 4 have multiplicative inverses in the ring
a. (Z6, +61-6)
b. (Z7, +7,-7)
c. (Q,+,.)
4. The ring
is a field.
a. (R - {0}, +,.)
b. (Z4, +4.4)
5. The set of odd integers is
c. (R, +,.)
with the usual addition and multiplication.
c. ring without identity
a. not ring
b. ring with identity
6. Every ideal in the ring (Z, +,.) is
a. principal
b. maximal
c. prime
7. Z1₁0 is
since 2 and 5 are zero divisors.
a. an integral domain b. not an integral domain
c. not ring
c. an integral domain ring
c. without identity](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F40a0ba46-1adc-40e4-bddc-e181d75a74f5%2F1bb35730-139b-43db-8bb6-aa5f3d0ab289%2Ffaki8x_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Q2: (A) Choose the correct answer for each of the following:
1. The cancellation law holds in
a. any ring
b. a commutative ring
2. The ring of even numbers (Ze, +, .) is.
a. with identity
b. with zero divisor
3. The elements 2 and 4 have multiplicative inverses in the ring
a. (Z6, +61-6)
b. (Z7, +7,-7)
c. (Q,+,.)
4. The ring
is a field.
a. (R - {0}, +,.)
b. (Z4, +4.4)
5. The set of odd integers is
c. (R, +,.)
with the usual addition and multiplication.
c. ring without identity
a. not ring
b. ring with identity
6. Every ideal in the ring (Z, +,.) is
a. principal
b. maximal
c. prime
7. Z1₁0 is
since 2 and 5 are zero divisors.
a. an integral domain b. not an integral domain
c. not ring
c. an integral domain ring
c. without identity
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