5
$\begingroup$

A question that's been bothering me:

R is a ring with unity. Also consider $M_n(R)$ the matrix ring.

If all ideals $J$ of $M_n(R)$ are finitely generated, does every ideal $I$ of $R$ need to be finitely generated?

  • 1
    Is that statement true for all $n$?2012-10-31
  • 0
    Yes, for all $n$.2012-10-31

2 Answers 2