Question

I is not finitely generated but all ideal containig i is finitely generated example

Answer 1

If I is an ideal in a ring R such that I is not finitely generated and every ideal properly containing I is finitely generated, then I is prime.

Let I be a non-finitely generated ideal and let a,b∈R such that a,b∉I. Then a∈I′ such that I′ is finitely generated and I′ properly contains I; b∈I′′ such that I′′ is finitely generated and I′′ properly contains I. I am having difficulties in showing that ab∉I.

Answer 2

Hey mate......

Here is the correct answer :

I is an imaginary word.......

I hope that it was helpful to you.............

If you want these type of answers..... so you can follow me