Abstract Algebra Answers

Every subring of a non-commutative ring is non-commutative.
State whether the given statement is true or false, give reason of your answer.

Is the given statement true or false, give reason of your answer ?
The characteristic of a field containing (50− 1) elements is 50.

State, with a reason, the given statement is true or false .
{ α1, α2, ...., αn } is a set only if all the αis
follow a given rule.

The function f ,defined by f(x) = (x-1)/(3-x) , has the same set as domain and as
range.
State the given statement is true or false, give reasons for your answer.

If (D,+,•) is an integral domain such that 1∈D , then D is a field.
State the given statement is true or false, give reasons for your answer.

Not every polynomial that is irreducible over Q[x] is irreducible over Z[x] .
State the given statement is true or false, give reasons for your answer.

If ( R ,*1,*2) is a ring, then ψ : R × R → R :ψ(r1,r2) = r1 *2 r1 is a binary operation.
State the given statement is true or false, give reasons for your answer.

Every subring of a non-commutative ring is non-commutative.
State the given statement is true or false, give reasons for your answer.

The characteristic of a field containing (50−1)elements is 50.
State the given statement is true or false, give reasons for your answer.

{α1 ,α2 , ….,αn} is a set only if all the αis
follow a given rule.
State the given statement is true or false, give reasons for your answer.