Gemara

16a (Mishnah): One may build with Nochrim Bimasi'os (this will be explained). When he gets to the dome where they put the idolatry, it is forbidden.

(R. Elazar): If he built it, the wages are permitted.

Question: The dome is merely Tashmish (something that services) Avodah Zarah. All agree that Tashmishei Avodah Zarah are not forbidden until they service idolatry!

(R. Yirmeyah): R. Elazar teaches that if he built idolatry itself, the wages are permitted.

Question: According to R. Akiva, who forbids idolatry immediately (even before it is served), why are the wages permitted?

Answer (Rabah bar Ula): It is considered idolatry only when it is completed, i.e. when the last hammer blow is done. The last blow is worth less than a Perutah;

He holds that wages accrue continuously from the beginning until the end. (We do not say that all the wages are due for the last blow/)

Kidushin 48a (Beraisa - R. Meir): If one said 'make this into rings, and I will be Mekudeshes to you', once he makes them, she is Mekudeshes;

Chachamim say, she must get (other) money to be Mekudeshes.

All agree that a loan cannot Mekadesh. They argue about wages. R. Meir holds that they are due at the moment it is completed. Chachamim hold that wages accrue from the start until the end.

Bava Basra 87a - Question: Why does the Mishnah say that one who detaches any amount of flax acquires it all?

Answer (Rav Sheshes): The case is, the seller said 'go make any improvement in the field and acquire it all.'

Rishonim

Rif (Avodah Zarah 5b): If he built the dome where they put the idolatry, the wages are permitted.

Rambam (Hilchos Avodah Zarah 7:5): If one builds idolatry for someone else, even though he is lashed, the wages are permitted. This is even if he made it for a Nochri, and it is forbidden immediately, for it is forbidden only once it is finished, and the last blow is worth less than a Perutah.

Ra'avad: This is according to the opinion that wages accrue continuously.

Rambam (9:11): One may not build with Nochrim a dome on which they stand up idolatry. If he transgressed and built it, the wages are permitted. l'Chatchilah, one may build the hall or Chatzer that houses the dome.

Beis Yosef (YD 143 DH u'Mah she'Chosav b'Shem): The Rambam explains that Bimasi'os are halls or Chatzeros that house the dome. Rashi explains that they are podiums on which they offer Korbanos to idolatry, i.e. Tashmish d'Tashmish (it services something that services idolatry). Tosfos rejected Rashi's Perush, for one may not build anything that services idolatry, even Tashmish d'Tashmish. Rather, the text is Dimasi'os, i.e. bathhouses.

Rosh (Avodah Zarah 1:19): Even if he built idolatry itself, the wages are permitted, for wages accrue continuously. In any case, one need not pay until the end, like it says in Bava Metzi'a.

Rosh (Kidushin 2:11): The Halachah is that wages accrue continuously. R. Elazar says so in Avodah Zarah, and no one argues.

Tosfos (19b DH Makosh): Even if the last blow is worth less than a Perutah, one may not benefit at all from idolatry! We must say that this is not called benefit, for he would have received his full wage even without the last hit.

Tosfos Rid (Kidushin 48a DH Yeshnah): Why can't one be Mekadesh a woman with the last Perutah of work, even if wages accrue continuously? Do not say that the first half of the last Perutah is a loan, for less than a Perutah is not a loan! Rather, also the last Perutah is a loan until she gets the Keli. The other opinion holds that wages are due only at the end, i.e. when she gets the Keli, so it is not a loan.

R. Yonah (Bava Basra 87a DH Hacha): The buyer acquires the field through Kinyan Kesef, i.e. what the seller owes him for improving the field. Since the entire job is worth a Perutah, we cannot say that wages accrue continuously. (i.e. a loan cannot be less than a Perutah).

Sha'ar ha'Melech (Hilchos Ishus 5:20 DH ul'Da'as): The Ra'avad holds that she is Mekudeshes once he finishes the Keli. How can he answer the Tosfos Rid's question? The Ra'avad, and even Rashi (who holds that she is Mekudeshes when she gets the Keli), can hold that even less than a Perutah can be a loan. How can the Tosfos Rid explain why wages of idolatry itself are permitted? The last Perutah is forbidden, and it is mixed with the wages! If we will say that he may benefit from all the wages except for a Perutah (similar to what the Tur (133) says in the name of the Ra'avad), why did the Gemara need to say that the last blow is not worth a Perutah? He must say that the Halachah does not follow R. Yirmeyah, rather, Rav Sheshes (Bava Basra 87a), who holds that when the entire job is worth a Perutah, we cannot say that wages accrue continuously. (I.e. Rav Sheshes holds that a loan cannot be less than a Perutah, and R. Yirmeyah disagrees.)

Poskim

Shulchan Aruch (YD 143:2): One may not build with a Nochri a dome on which they stand up idolatry. If he transgressed and built it (Rema -or even idolatry itself), the wages are permitted. L'Chatchilah, one may build the hall or Chatzer that houses the dome.

Taz (3): Even the opinion that idolatry is forbidden immediately (once it is finished) agrees that the wages are permitted, for wages accrue continuously, and the last hammer blow is worth less than a Perutah. All the Poskim say so. The Rif, Tur and Shulchan Aruch omitted this. It seems that they did not want to reveal this Heter, so people will stay far from this despised Aveirah. We say similarly (Shabbos 153b) 'there was another Heter, but Chachamim did not want to reveal it.'

Taz (4): The Tur brought Tosfos, who says that there is no Heter for Tashmish d'Tashmish. Why weren't the Shulchan Aruch and Rema stringent for this opinion? We find that Chachamim were extra stringent about idols! E.g. we may not sell even parchments and ink (lest they use them to write Sifrei Avodah Zarah - Rema 139:15). All the more so one should not build the hall or Chatzer that houses the dome! I say that even Rashi and the Rambam permit only to help. The Mishnah says that one may build with them. The Rambam forbids building the dome with them, and similarly permits building the hall with them. We often find that help is insignificant. All forbid to build by himself. Surely one should rule like the Ri, who saw Rashi and disagreed. We should stay far from what is despised or what resembles it.

Bach (3): The Rosh, Ran, Tosfos and Rambam permit the wages even if he built idolatry itself. Why did the Tur omit this? It seems that he is stringent like the Rif, who brought R. Elazar's law Stam. He permits wages for the dome, but forbids wages for idolatry itself. The Gemara said that the Chidush is to permit the wages of idolatry itself, but we hold unlike R. Yirmeyah. Even though we hold that wages accrue continuously, even to be lenient about Kidushin, like the Rif and Rambam say, we do not permit just because the last blow is not worth a Perutah. One may not benefit from idolatry, even less than a Perutah! Money of idolatry is mixed with the wages. Tosfos gave a difficult answer. The Rif does not rely on this. Rather, we rule simply like R. Elazar. What is the Chidush? All agree that Tashmishei Avodah Zarah are not forbidden mid'Oraisa until they are served! The Chidush is that the wages are permitted even mid'Rabanan. We hold like the Rif and Tur, even though the Rema was lenient.

Rebuttal (Shach 4): The Bach's answer for the Tur and Rif is astounding. We cannot argue with the Gemara based on reasoning, especially since Tosfos answered the question! Rather, the Rif learned from the Yerushalmi (Halachah 7). R. Elazar says that if he built it, it is permitted. R. Mana forbids, for he is happy about the idolatry as long as the dome lasts. R. Elazar teaches unlike R. Mana. This is his Chidush. There is no source to say that he permits wages of idolatry itself! We always rule like the Bavli when it argues with the Yerushalmi, but here the Yerushalmi proves that R. Yirmeyah's Perush of R. Elazar is wrong. Had R. Yirmeyah heard that R. Mana argues, he would not have given his answer. The Rosh, Ran, Rambam and Rashba rule like R. Yirmeyah. Why did the Bach question the Rema? He rules like the Bavli and great Poskim. The Yerushalmi is not difficult. We can say that R. Elazar permits even wages of idolatry itself, and R. Mana forbids even wages of the dome. The Bavli holds that obviously wages for the dome are permitted; it rejects R. Mana.

Rebuttal (Sha'ar ha'Melech ibid., DH va'Ani): The Tur (133) said in the name of the Ra'avad that if one was hired to move 100 barrels for 50 Perutos and one barrel was of Yayin Nesech, the wages are permitted even though a half Perutah is from Yayin Nesech. The Rashba says that the Ra'avad learned from R. Yirmeyah. The Tur did not bring an opposing opinion. We cannot say that the Tur forbids due to less than a Perutah of Isur mixed in, unlike R. Yirmeyah! Rather, we can answer like I said above. He rules like Rav Sheshes. Wages of idolatry itself are forbidden due to the last Perutah.