Ideal T or F Flashcards
1
Q
Every prime ideal of every commutative ring with unity is a maximal ideal.
A
F
2
Q
Every maximal ideal of every commutative ring with unity is a prime ideal.
A
T
3
Q
Q is its own prime subfield.
A
T
4
Q
The prime subfield of C is R.
A
F
5
Q
Every field contains a subfield isomorphic to a prime field.
A
T
6
Q
A ring with zero divisors may contain one of the prime fields as a subring.
A
T
7
Q
Every field of characteristic zero contains a subfield isomorphic to Q.
A
T
8
Q
Let F be a field. Since F[x] has no divisors of 0, every ideal of F[x] is a prime ideal.
A
F
9
Q
Let F be a field. Every ideal of F[x] is a principal ideal.
A
T
10
Q
Let F be a field. Every principal ideal of F[x] is a maximal ideal.
A
F
