Homework assignments for Math 28b, Spring 1998


Problem Set 1. Due Thursday, Jan. 29, 1998

  1. Page 175: B1,B4 (see page 170 of the book for the definition of F(R).)
  2. Page 179: K1,K2,K4.
  3. Let B consist of all matrices where a and b are real numbers. Is B a subring of M2(R)? Is B a field? Explain.
  4. Let R be a ring with unity, and let R* denote the set of invertible elements. Show that R* is a group, where the group operation is the multiplication in the ring. (You may want to refer to problem I.1-5 on page 178.)
  5. Let B consist of all matrices where a,b,c,d,e,f are in Z5, Show that B is a subring of M3( Z5). How many elements are there in B*? Write down a subgroup of B* of order 125.