Gemara

Question (Ravina): Can a man be a Shali'ach for his wife to permit a Neder through regret? (Ravina wanted to do so for his wife.).

Answer (Rav Ashi): He may do so only if he finds (three) people already gathered. If not, he may not assemble a Beis Din to permit it.

We learn three things from this:

A man can be a Shali'ach for his wife's regret;

One cannot permit a Neder in his Rebbi's region;

A man can be a Shali'ach for his wife's regret only if three are already gathered.

Mishnah (Nega'im 2:5): One can permit any vow, except for his own;

R. Yehudah says, also one cannot permit his wife's vow Beinah l'Vein Acherim (between her and others).

One can inspect (a Mum on) any Bechor, except for his own.

Rishonim

The Rif and Rosh (1:7) bring the Gemara.

Rosh (citing the Re'em): Ravina's wife had asked Ravina to permit her vow. The Halachah follows Chachamim, who say that one can permit any vow except for his own. Ravina wanted to honor his Rebbi, so he asked Rav Ashi, unknown to his wife.

Korban Nesan'el (70): Here, the Rosh cites the Re'em. The Rosh himself (11:1, brought below) says that a husband cannot permit his wife's vow. He must say that Ravina's wife did not know the Halachah.

Rosh (11:1): The Yerushalmi says that one cannot permit his wife's Neder if it is Beino l'Veinah (between them). It is like his own Neder! R. Chiya switches the opinions in the Mishnah (Nega'im 2:5), so that Chachamim say that he cannot permit it. This is the Halachah. Ishto k'Gufo (one's wife is like himself), and one cannot permit his own vow.

Ramban (on Rif 25b, and Rivash 406): The Yerushalmi says that one cannot permit his wife's Neder if it is Beino l'Veinah, for it affects him. This is like one who forbade his property to people of his city; a Chacham of the city cannot permit it.

Question (Beis Yosef YD 228 DH Mi she'Omar): One is not disqualified from permitting his own vows because it affects him. Rather, the Torah decreed "Lo Yachel Devaro" - only others may permit him! Our text of the Yerushalmi suggests that if Levi forbade himself benefit from people of his city, a Chacham of the city can permit it. This is unreasonable. The Chacham benefits Levi! Rather, we must explain that a Chacham of the city cannot permit Levi when Levi forbade himself from people of his city, for the Chacham benefits Levi.

Answer (Taz 8): If one stands to gain from permitting a vow, he is disqualified, just like he cannot permit his own vow. We are concerned lest he not investigate well enough. This is like a judge: he cannot judge a case if he might gain from the outcome.

Ramban (on Rif 25b): We inferred from Ravina that one may not permit a vow in his Rebbi's region. Even though he himself could not have permitted his wife's vow, he could have asked his Talmidim to do so.

Ritva: My Rebbi says that even though Ravina himself could not have permitted it, he could have joined two others to permit it. One cannot permit his own Bechor, but he can permit it with two others (Bechoros 31a). R. Shimshon (on Nega'im 2:5) explained like this.

Hagahah (on R. Shimshon): We cannot learn from Bechor! One cannot permit his own Bechor because he is suspected to lie. We are not concerned for this when he is with two others. The Torah decrees that one cannot permit his own vow. He cannot permit his wife's vow, for Ishto k'Gufo. Three commoners are in place of one Chacham. If he is one of the three, it is as if only two permit her!

Rivash (406): (Presumably, the Ramban holds that) Ravina could not have permitted her vow even with two others, just like one cannot join to permit his own vow.

Note: Hagahos Maimoniyos (Hilchos Shevuos 6:2) cites a text in which Ravina's wife had been excommunicated, and he wanted to be a Shali'ach to permit her. According to this, we cannot infer whether or not one may permit his wife's vow.

Rambam (Hilchos Shevuos 6:3): One cannot permit his own oath.

Poskim

Shulchan Aruch (YD 234:56): A husband cannot join two to permit his wife's vow.

Beis Yosef (DH u'Mah she'Chosav sheha'Rosh): The Ran is unsure whether or not one can join two others to permit his wife's vow. The Tur says that he cannot. This is because Ishto k'Gufo, and one cannot join to permit his own vow. The Rashba (7:145) leans to rule like Chachamim, even though the Ramban rules like R. Yehudah. I do not know why the Tur says that the Rambam rules like R. Yehudah. In Hilchos Shevuos (6:3), he wrote like Chachamim's words!

Birkei Yosef (6 DH vehaTur): Also in Perush ha'Mishnayos the Rambam rules like Chachamim. The Rashba proved from Ravina that a husband can permit his wife's vow, but he was reluctant to be lenient against one with seniority, i.e. the Ramban. The Ramban refuted the Rashba's support, by saying that Ravina could have asked three others to permit her vow! It seems that the Rashba rejects this. He holds that if the Bavli agreed that the opinions in the Mishnah should be switched, it would have said so, lest we err. Rather, the Bavli accepts the text, that Chachamim allow permitting one's wife's vow, and the Halachah follows them.

Bach (DH v'Nir'eh): The Tur's text of the Rambam said 'a man cannot permit his own vow or his wife's vow.' The Rambam (6:6) says that one can permit his relative's vow. He does not say so about his wife, for Ishto k'Gufo.

Mar'eh ha'Panim (Nedarim 35a DH Rebbi): The Tur learns from the way the Rambam explains Ravina's question (and the answer). No one else can be a Shali'ach for regret. We are lenient only to allow a husband, for Ishto k'Gufo. All the more so we are stringent to consider Ishto k'Gufo to teach that he cannot permit her vow!

Chasdei David (Nega'im 1:10 b'Sof, DH ul'Inyan Nedarim): "Lo Yachel Devaro (his word)" teaches that one cannot permit his own vow. Perhaps if a man affirmed or was silent to his wife's vow, it is called Devaro.

Ma'ase Roke'ach (Shevuos 6:3): The Rambam did not say that one cannot permit 'Shevuaso', rather, 'Shevuas Atzmo', to include his wife's vow. Rav Ashi did not tell Ravina 'you do not need Shelichus. You can permit it with two others (it suffices for one of the three judges to know the vow).' This suggests that a husband cannot permit even with two others. Perhaps the Tur learns like the Radvaz, who explains that the end of Halachah 4, in which the Rambam says 'a husband cannot be a Shali'ach to permit his wife's vow', is imprecise. He means that the husband cannot permit her vow.

Gra (107): Perush ha'Rosh (8b DH Asa) says that even according to R. Yehudah, Ravina could have asked three others to permit her vow. This shows that he holds that the husband cannot be among the three.

Shulchan Aruch (ibid.): A father can join two to permit his daughter's vow.

Gra (108): We learn from Rav Nachman (77b, who says that we can permit vows of relatives).