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 ![](Image593.gif)
- Show that if
![](Image594.gif)
is a homomorphism of rings then:
is an ideal of ![](Image596.gif)
is a subring of ![](Image598.gif)
- Find all possible rings with:
- 2 elements.
- (G)
4 elements.
- Let
![](Image599.gif)
be a commutative ring with 1.
- Show any maximal ideal M, is a prime ideal.
- (G)
If ![](Image600.gif)
is finite, show that any prime ideal is maximal.