# Math Help - ideal problem....

1. ## ideal problem....

Q:A ring R has maximum ideals
a)if R is infinite
b)if R is finite
c)if R is finite atleast 2 elements
d)only if R is finite

2. ## Not sure I understand

Is only one allowed to be true? I havent thought about the others, and I cannot be positive that all infinite rings posses maximum ideals, but certainly the following does.

Consider a polynomial ring with coefficients from a field $\mathbb{F}$. $\mathbb{F}[x]$ is an infinite ring a Principal Ideal Domain and any irreducible polynomial forms a maximal ideal since in PIDs irreducible implies prime which implies maximal.

3. Originally Posted by Mathventure

Q:A ring R has maximum ideals

a) if R is infinite

b) if R is finite

c) if R is finite at least 2 elements

d) only if R is finite
c) is the answer. (no more explaining from me! that kind of asking question deserves this kind of answer!)