# Algebra – II MCQs

1…………………. is a non-commutative ring .

a. NONE

b. z

c. M2

d. Q

2.Zp is not a field if p is ………………

a. NOT PRIME

b.

c.

d. PRIME

3.Every integral domain can be imbedded in a ……………….

a. FIELD

b. Z

c. Q

d. RING

4.In ring Z …………… is not invertible element .

a. 1

b. NONE

c. 2

d. 3

5.A commutative ring is field ?

a.

b. FALSE

c. TRUE

d.

6.A ring R is called boolean if a^2 =

a. a^2

b. a^3

c. negative a

d. a

7.Zero divisor in z6 are

a. 2&1

b. 2&4

c. 2&3

d. 2&5

8.Is z4 is Field or not ?

a. yes

b.

c.

d. not

9.Center of ring is …………of R

a. ideal

b. field

c. sub ring

d. not ideal

10.If I and J are ideals then I+J is

a.

b. sub ring

c. ideal

d. fielf

11.If R is commutative ring then centre of R =

a. R^2

b. field

c. z

d. R

12.If I is ideal in R then R/I is called

a. c®

b. Quotient ring

c. field

d. ring

13.Is ring of integers a principal ideal

a. yes

b.

c. no

d.

14.which of following is vector space

a. R over R

b. Z over R

c. Q over R

d. R over C

15.V is called direct sum of U and V if intersection of u and v is

a.

b.

c. empty

d. none empty

16.dim u – dim v =

a. dim u

b. dim v

c. dium u/v

d. dim uv

17.if T:v→ v is linear transformation then E lembda is ……

a.

b. sub space

c. not sub space

d.

18.characteristics of the ring Z2*Z4*Z6

a. 4

b. 2

c. 12

d. 6

19.number of a prime ideal Z105

a. 6

b. 4

c. 2

d. 8

20.Which of the following is a prime ideal

a. 5z

b.

c. both

d. 3z

21.The ideal R of a ring R is called

a. none

b. singleton ideal

c. zero ideal

d. unit ideal

22.The idempotent of an element Z6 is .

a. 5

b. 4

c. 3

d. 6

23.A field having no proper subfield is,

a. division ring

b. prime field

c. none

d. ring

24.A ring having no proper ideals is called

a. none

b. sub ring

c. complex ring

d. field

25.The integral domain of which cardinality is NOT possible

a. 6

b. 5

c. 7

d. 8

26.The intersection of two subrings of a ring is

a.

b. sub ring

c. not sub ring

d.

27.Every ring possesses two improper

a. subideal

b. sub field

c. ideal

d. none

28.A commutative ring without zero divisior CAN be imbedded in

a. ring

b. both

c. FIELD

d. none

29.The set of residue classes (modulo n) is a ring without zero divisor wrto addition and multiplication, iff n is

a. even

b. odd

c. pime

d. none

30.the idempotent element of Z6 is:

a. 4

b.

c. 3

d. 5

31.which of the following is a divisor ring?

a. Q

b. Z

c. E

d. none

32.A homomorphism ᵩ;RàR’ ,Ker ᵩ ={0} then ᵩ is:

a. surjective

b. bijective

c. injective

d. none

33.if R be a ring and R/P is an integral domain then P is :

a. prime ideal

b.

c. division ring

d.

34.Every maximal ideal of commutative ring with identity is a:

a. prime ideal

b.

c. division ring

d.

35.the characteristic of ring of integers is :

a. 0

b. 2

c. 6

d.

36.Z6 is a zero divisor

a.

b. TRUE

c. FALSE

d.

37.the elements 3 and 5 are units in ring….?

a. Z11

b. Z14

c. Z6

d. Z9

38.which one is a simple ring?

a.

b. Z5

c. N

d. Z

39.which of the following is (are) field(s)?

a. ALL

b. R

c. C

d. Q

40.The number of unit element of ring Z is:

a. 2

b. 1

c. INFINITE

d. 3

41.A ring (Q,+,.) , (R,+,.) and (C,+,.) where Q,R and C are called

a. RING

b. NONE

c. GROUP

d. FIELD

42.singelton {0} is a ring with respect to

a. MULTIPICATION

b.

c. BOTH

43.the characteristic of a ring (z3, +3,*3)

a. 3

b. 2

c. 1

d. 0

44.which of the following is finite field

a. Z10

b. Z7

c. Z8

d. Z9

45.Minimum number of elements in a field is

a. 2

b. 3

c. 4

d. 5

46..the number of unit element of ring z is

a. 2

b. 1

c. 3

d. 4

47.the characteristic of an integraal domain is

a. EITHER 02 OR PRIME

b. EITHER 0 3OR PRIME

c. EITHER 1 OR PRIME

d. EITHER 0 OR PRIME

48.the intersection of two ideal is

a. RIGHT IDEAL

b. NONE

c. LEFT IDEAL RIGHT IDEAL

d. IDEAL

49.A commutative ring with Unity is a field if it is

a. NO PROPER IDEAL

b.

c.

d. PROPER IDEAL

50.which of the following is not a ring?

a. (Z,+,*)

b. (N,+,*)

c. (Q,+,*)

d. NONE