Correctamundo.
So when the woman saw that the tree was good for food, that it was pleasant to the eyes, and a tree desirable to make one wise, she took of its fruit and ate. She also gave to her husband with her, and he ate.
Genesis 3:6
Nothing in that indicates that Adam was even present at the point of Eve's temptation. Maybe I'm perceiving this differently, but the way I always saw it:
1. The snake tempts Eve alone.
2. Eve, knowing full well what God had told her, took the fruit and ate.
3. She returns to Adam, gives him the fruit without telling him what it was, and he unknowingly ate.
Now, the huge gaps in the narrative lead me to think it's more of a euphemism for sex (after all, what body part represents a serpent that can transform into an arm holding an apple?), but if we're going to take this literally, the only sin on Adam was one of ignorance.
Also: nothing in the scripture up to this point indicates Adam being assigned lordship over Eve; she was created as a companion, not a subject. The lordship was Eve's punishment for deceiving Adam.