Math 420/620
Homework 7
- a) Let be a Boolean ring (that is, ). Show that is commutative.
b) (G) Give an example of a Boolean ring that has no identity.
- Let be (left) ideals of . Show that is also a (left) ideal.
- Assume that is a ring homomorphism with . Show that
- Show that if
is a homomorphism of rings then:
- is an ideal of
- is a subring of
- Find all possible rings with:
- 2 elements.
- (G)
4 elements.
- Let
be a commutative ring with 1.
- Show any maximal ideal M, is a prime ideal.
- (G)
If
is finite, show that any prime ideal is maximal.