Q2: (A) Choose the correct answer for each of the following:1. The cancellation law holds ina. any ringb. a commutative ring2. The ring of even numbers (Ze, +, .) is.a. with identityb. with zero divisor3. The elements 2 and 4 have multiplicative inverses in the ringa. (Z6, +61-6)b. (Z7, +7,-7)c. (Q,+,.)4. The ringis a field.a. (R - {0}, +,.)b. (Z4, +4.4)5. The set of odd integers isc. (R, +,.)with the usual addition and multiplication.c. ring without identitya. not ringb. ring with identity6. Every ideal in the ring (Z, +,.) isa. principalb. maximalc. prime7. Z1₁0 issince 2 and 5 are zero divisors.a. an integral domain b. not an integral domainc. not ringc. an integral domain ringc. without identity

Answer 1: Must know:The cancellation laws hold in a ring R if an only if R has no zero divisors

Answered: Q2: (A) Choose the correct answer for…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter5: Rings, Integral Domains, And Fields

Section5.1: Definition Of A Ring

Problem 33E: Consider the set S={ [ 0 ],[ 2 ],[ 4 ],[ 6 ],[ 8 ],[ 10 ],[ 12 ],[ 14 ],[ 16 ] }18. Using addition...

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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 c. an integral domain ring