Mr Maths

Mr Maths Union of all singletons is the Universe�

27/07/2023

Find true statements

a) Any commutative skew field is a field
b) Any ring with prime order is a field
c) Any finite integral domain is a field
d) Any ring which is both integral domain and skew field, is a field

22/07/2023

A function f:A-->B is one-one if for x,y€A

a) x=y implies f(x)=f(y)
b) x implies f(x) (y)
c) f(x) (y) implies x
d) f(x)=f(y) implies x=y

Here the symbol # means not equal

12/07/2023

Pick the true statements

a) Every cycle is a permutation
b) Every permutation is a cycle
c) Every transposition is a cycle
d) Every transposition is a permutation

11/07/2023

Which of the followings are true?

a) Subgroup of an abelian group is abelian
b) Subgroup of an infinite group is infinite
c) Subgroup of a cyclic group is cyclic
d) Subgroup of a non-abelian group is non-abelian

16/08/2021

Let D be an integral domain. x,u€D.
Then which of the followings are true?

a) If x is an irreducible and u is a unit then ux is irreducible

b) If x and u are irreducible then ux is irreducible

c) If x is reducible and u is a unit then ux can be irreducible

d) If x and u are reducible then ux is reducible

15/08/2021

Z(X) is

a) Unique factorization domain
b) Euclidean domain
c) Principal ideal domain
d) Noetherian domain

10/07/2021

True or False

There is an integral domain of order 10.

27/06/2021

Prove or disprove

A subring of a ring with unity e can have a unity different from e.

27/06/2021

True or False

Let R be a commutative ring. R has the cancellation property under multiplication if and only if R has no zero divisors.

22/06/2021

Let R be a ring. Which of the followings are subrings of R?

a) {x€R | ax=0} for a€R

b) {x€R | ax=0 or xa=0} for a€R

c) {x€R | xa=ax for all a€R}.

27/05/2021

Pick the true statements

a) Every finite group has finite number of subgroups.

b) Every infinite group has infinite number of subgroups.

c) If a group has only finite number of subgroups then the group itself finite.

d) If a group has infinite number of subgroups then the group itself infinite.

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