Homework assignments for Math 28b, Spring 1998
Problem Set 1. Due Thursday, Jan. 29, 1998
 Page 175: B1,B4 (see page 170 of the book for the definition of F(R).)
 Page 179: K1,K2,K4.
 Let B consist of all matrices
where a and b are real numbers. Is B a subring of M_{2}(R)?
Is B a field? Explain.
 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.15 on page 178.)

Let B consist of all matrices
where a,b,c,d,e,f are in Z_{5}, Show that B is a subring of M_{3}( Z_{5}). How many elements are there in B^{*}? Write down a subgroup of B^{*} of order 125.