In accordance with whose opinion among the tanna’im does Rav’s halakha correspond? It is in accordance with the opinion of R' Meir, who said as a principle that the hand of a woman is like the hand of her husband. According to R' Meir, a slave has no independent right of acquisition, and anything given to a slave belongs to his master even if it was stipulated otherwise (see Kiddushin 23b). Rav assumes that similarly, a married woman has no independent right of acquisition, but rather, anything that she attempts to acquire for herself is automatically acquired by her husband.
ורמינהו: כיצד משתתפין במבוי? מניח את החבית ואומר: הרי זה לכל בני מבוי. ומזכה להן על ידי עבדו ושפחתו העברים, ועל ידי בנו ובתו הגדולים, ועל ידי אשתו.
R' Zeira continues: And raise a contradiction from an unattributed Mishnah (Eiruvin 73b), which presumably follows the opinion of R' Meir: How does one merge the courtyards that open into an alleyway in order to permit its residents to carry on Shabbat from one courtyard to another in the same alley, if a person wishes to act on behalf of all the residents of the alleyway? He places a jug filled with his own food or wine and says: This is for all the residents of the alleyway. For this gift to be acquired by the others, someone must accept it on their behalf, and the tanna therefore teaches that he may transfer possession to them even by means of his Hebrew slave or female slave, whom he does not own, and likewise by means of his adult son or daughter, and similarly by means of his wife. These people may acquire the eiruv food on behalf of all the residents of the alleyway.