Quick basic grammar question.
With respect to expressing ownership of an item using ある. Am I correctly understanding the general meaning and particle use in the following sentences?
私の辞書がありません → I do not have MY dictionary
私は辞書がありません → I do not have a dictionary
I think the second example makes sense grammatically speaking, however I'm unsure if the first example is correct. Can I use の in similar situations like this to express if a particular item belongs to me? Can I use it like this with いる as well?
私の子供がいます → The child is mine
私は子供がいます → I have a child