Many studies have been conducted to characterize commutative rings whose finitely generated modules are direct sums of cyclic modules (called FGC rings). We study FGC rings in some special cases. We characterize Noetherian duo FGC rings. Another family of rings whose certain modules are direct sums of cyclic modules is the family of rings which ideals are direct sums of cyclic modules. To study intended rings, we define and study local dimension. Next, we study commutative rings with countable local dimension which ideals are direct sums of cyclic modules.
