Math 420/620

Homework 7

 

  1. a) Let be a Boolean ring (that is, ). Show that is commutative.

    2. b) (G) Give an example of a Boolean ring that has no identity.

     

  2. Let be (left) ideals of . Show that is also a (left) ideal.

    3.  

  3. Assume that is a ring homomorphism with . Show that

    4.  

  4. Show that if
is a homomorphism of rings then:
  1. is an ideal of
  2. is a subring of

 

  1. Find all possible rings with:
  1. 2 elements.
  2. (G) 4 elements.

 

  1. Let
be a commutative ring with 1.
  1. Show any maximal ideal M, is a prime ideal.
  2. (G) If
is finite, show that any prime ideal is maximal.