# Math Help - noetherian ring help

1. ## noetherian ring help

Could you please help or even just give me some advice. I have to prove/disprove the claim that every finite ring is noetherian.
I know that a ring R is noetherian, if every ideal of R is ﬁnitely generated. Also I know there are many infinite rings which are noetherian such as the integers or afield like the complex numbers.

Thanks if anyone can help me in proving this.

2. ## Re: noetherian ring help

If an ideal of R is not finitely generated, does that not imply an infinite number of elements in the ring R?, since what does it mean for a Ideal to be generated by elements?
There exists a set of $a_1,...,a_n \in I$ such that I = $\{a_1R + ... + a_nR\}$. if $a_1,...,a_k \in I$ forms an infinite set, since $I \subset R$, $a_1,...a_k \in R$, so R must be infinite.