Pretty much, yeah. It's like the old law in some of the Celtic countries, where, if the land was owned at all (it wasn't always, not in the sense of 'could be bought, sold or otherwise freely disposed of'), it was generally owned by a man. That is barring such events as widowhood or a family having only female heirs. Which, by the way, is why in the ballads and folktales, marrying a widow or a female only child was generally considered a good deal, because she usually came with land as well as property.
However, women owned the domestic property, the portable 'plant' of a household, and often also flocks and herds. When a woman married away from her family, she took with her such things as, say, her flocks of sheep and poultry, her spinning and weaving gear, sewing materials, cooking and dairy equipment, blankets and other such. Her family might add their gifts, and the prospective husband was supposed to make a contribution to her general property, which actually was not so much 'hers' as it was the property of the female line of her family, to be added to during her lifetime and divided among her daughters.
If a couple divorced, the woman took her stuff with her, often with an addition by her husband if he had been at fault, or if she felt herself responsible, she might choose to leave part of her possessions to her husband, or the local brehon (lawgiver) might impose that on her as a fine.
Generally that old system worked pretty well, to the point that some old families still used when I was a kid.
