GR0568 Probelm 40

Forum for the GRE subject test in mathematics.
phcooh
Posts: 4
Joined: Mon Oct 13, 2008 7:15 pm

GR0568 Probelm 40

Postby phcooh » Mon Oct 13, 2008 7:26 pm

for which of the following rings is it possible for the product of two non-zero elements to be zero?
a. ring of complex numbers
b. ring of integers modulo 11
c. ring of continuous real-valued functions on [0,1]
d. ring {a+b(2^1/2): a, b are rational numbers}
e. ring of polynomials in x with real coefficients

answer is c.
could someone explain please?
Thanks a lot.

Nameless
Posts: 128
Joined: Sun Aug 31, 2008 4:42 pm

Postby Nameless » Mon Oct 13, 2008 9:32 pm

Hi
there are some facts you need to know :
if F is a field then there is no zero divisor in F so a, b, d are incorrect
if R is a domain then R[x] - the ring of polynomial - is a domain also so R[x] has no zero divisor - hence e is incorrect.

so the answer is c.

By the way, we can find two non-zero functions f, g in C[0,1] st : f.g=0.

JcraigMSU
Posts: 13
Joined: Wed Aug 06, 2008 9:25 am

Postby JcraigMSU » Tue Oct 14, 2008 12:22 am

sure g(x) = 1, f(x) = 1-x




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