Mathematics 893 Problem Set 6

Suggested reading: Chapter 7, sections 1-4 and 6. Chapter 8, section 1.

Solutions due Friday November 4.

(a) Page 231 # 15, 16

(b) Page 233 #29, 30 Is the ring structure of A needed in #29?

(c) Page 237 #1

(d) Page 238 #2

(e) Find a maximal left ideal in the ring M_{3}(ℚ).

(f) Page 248 #10 Notes: In (b) pointwise addition of functions means that the function f + g is defined by (f + g)(a) = f(a) + g(a) for all a ∈ A. We will omit section 7.5 for now, but might come back to it later. Theorem 8(1), page 246, seems to be OK after all in the category of rings with unit, in spite of my note in Problem Set 5.