Is the marital relationship one of ownership, for the woman over the man, or for the man over the woman? And does a husband's statement to his wife, "You are not mine," constitute a divorce, taking into consideration the intention when the details of the situation are forgotten?

The husband's statement to his wife, "You are not mine," is an allusive (kinayah) divorce statement, and divorce does not occur by it unless he intended it. If he intended divorce by it, then it occurs; otherwise, it does not. If he forgets his intention, the default is that it was absent, and doubt is not taken into consideration.