Ring Theory And Field MCQs

Ring Theory And Field Quiz Outline

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Created on January 05, 2022 By

Quizllc

Ring Theory And Field MCQs

1 / 20

Euclidean Domain posses ?

Unity

U.F.D

Field

Principal Ideal Domain

2 / 20

A ring in which every prime ideal is irreducible?

Integers

Both A & B

3 / 20

Every integral domain is field?

True

False

4 / 20

Every integral domain is a field?

Infinite

Finite

Ring

None of these

5 / 20

Set of continuous real valued function form a field?

YES

6 / 20

Example of ring with zero divisors is?

Integers

Real numbers

Set of all 2 by 2 matrices

7 / 20

Unit element and unity element of ring considered as identical?

Yes

8 / 20

Is set of integers is an ideal of set of rationals?

Yes

9 / 20

Examples of ring with identity is?

Ring of integers

Ring of rational numbers

Ring Real numbe4rs

All of these

10 / 20

The nilpotent element in Z4 is?

None of these

11 / 20

Is every idempotent element is nilpotent?

Yes

12 / 20

If I and J be any two ideal of the ring R then their sum is?

Ring

Ideal

Not an ideal

Integral domain

13 / 20

The set of all 2 by 2 non-singular matrices form a?

Field

Integral domain Ring

Ring

Both A & C

14 / 20

The Zp ,where p is a prime nmber is?

Field

Ring

Integral Domain

All of these

15 / 20

A commutative ring with identity without zero divisors is called?

Field

Ring

Integral Domain

All of these

16 / 20

Z6 is the ring with zero divisors which of the following identify it?

1&4

3&2

4&7

9&5

17 / 20

Every ideal is a ?

Subring

Always not a subring

Unique factorization Domain

Prime ideal

18 / 20

The set ‘E’ of even integers is a ring?

With identity

Non-commutative ring

Without identity

Integral domain

19 / 20

Intersection of any two ideals is?

Subring

Ideal

Not an ideal

20 / 20

Centre of the ideal I is ?

Subset

Subring

Not a Subring

None of the above

Your score is

The average score is 63%

Ring Theory And Field MCQs with Answers

If An element a of ring R and an = 0 then nis called.

A. Nil- radial
B. Idempotent
C. Irreduciable
View Answer

A. Nil- radial

Is every idempotent element is nilpotent.

A. Yes
B. No
View Answer

B. No

The nilpotent element in Z4 is.

A. 2
B. 3
C. None of these
View Answer

A. 2

Examples of ring with identity is.

A. Ring of integers
B. Ring of rational numbers
C. Ring Real numbe4rs
D. Allof these
View Answer

D. Allof these

Is set of integers is an ideal of set of rationals.

A. Yes
B. No
View Answer

B. No

Unit element and unity element of ring considered as identical.

A. Yes
B. No
View Answer

B. No

Which of the following is the axioms of an ideal ,for any two elements ‘a’ and ‘b’ of ideal.

A. A-b is an element of ideal
B. Ab is an element of ideal,
C. Both A & B
View Answer

A. A-b is an element of ideal

The Ring of integers module n is field for.

A. All n.
B. Only prime numbers
C. Only even numbers
View Answer

B. Only prime numbers

If f: R → R’ is an epimorphism then the set of all those elements of R which are mapped onto the identity element of R’ is called .

A. Centre
B. Ring
C. Ideal
D. Kernal of f
View Answer

D. Kernal of f

Example of ring with zero divisors is.

A. Integers
B. Real numbers
C. Set of all 2 by 2 matrices
View Answer

C. Set of all 2 by 2 matrices