<m>∩<n>=<b> , b=gcd⁡(m ,n )

<m>∩<n>=<b> , b=m .n

<m>∩<n>=<b> , b=m/n

<m>∩<n>=<b> , b=Lcm⁡(m ,n )

Z

Z_p

M_2

Z × ZZ × Z

4 Z× Z

3 Z× 6 Z

2 Z×4 Z

Z× 3 Z

Maximal ideal

Prime ideal

Both

None of these

117 Z

113 Z

91 Z

69 Z

Prime

Maximal

Both

Neither prime nor maximal

R/M need not to be integral domain

R/M has zero divisor

R/M is division ring

None of these

For any ring R, every maximal ideal is a prime ideal

For any commutative ring with unity, every prime ideal is a maximal ideal

For any finite commutative ring with unity, every prime ideal need not to be a maximal ideal

For any commutative ring R, if R/P is an integral domain, p-Ideal, then P is prime ideal

Sum of two prime ideals is a prime ideal

Sum of two maximal ideals is a maximal ideal

Intersection of two prime ideals need not to be prime ideal

Intersection of two maximal ideals is a maximal ideal

Every proper prime ideal need not to be a maximal ideal

Every proper prime ideal P of R is maximal ideal

Every maximal ideal is prime ideal

None of these

I∩J is prime ideal

I.J is prime ideal

I∩J is not maximal ideal

I.J is maximal ideal

3

6

9

27

It is one-one homomorphism

It is onto homomorphism

Its kernel is not equal to zero

None of these

Need not to be a prime ideal

Need not to be an ideal

May be maximal ideal

Is prime ideal

Maximal ideal

Need not to be ideal

May be prime

May not be maximal

2

1

0

none

1

0

2

none

f(x)= [X x X]

f(x)= 0

f(a-ib)=a+ib

f(a+ib)=a-ib

3

0

1

None