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.
GR0568 Probelm 40
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.
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.