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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,+,.) c. an integral domain ring c. without identity

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,+,.) c. an integral domain ring c. without identity

Advanced Engineering Mathematics
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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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, +44) 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. Z10 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
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, +44) 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. Z10 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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