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?
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?