189-235A: Basic Algebra I
Due: Wednesday, October 8.
1. Page 162, 3.33.
2-5. Page 171, 3.34, 3.40, 3.41, 3.43.
6-7. Page 178, 3.45, 3.46.
8. Let F be
a field having infinitely many different elements.
a) If f and g are two polynomials with coefficients in
F, show that
if f(x)=g(x) for all x in F, then
f=g (as polynomials).
b) Show that this theorem continues to hold if F is
only assumed to be a
domain (having infinitely many elements) and not necessarily a field.
c) Show (by giving an example)
that the conclusion of a) can fail if F is a field with finitely many